{"id":665154,"date":"2023-07-19T17:03:48","date_gmt":"2023-07-19T11:33:48","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=665154"},"modified":"2023-07-19T17:04:03","modified_gmt":"2023-07-19T11:34:03","slug":"trigonometric-identity","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/","title":{"rendered":"Trigonometric Identity"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Introduction_to_Trigonometric_Identities\" title=\"Introduction to Trigonometric Identities\">Introduction to Trigonometric Identities<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Pythagorean_Identities\" title=\"Pythagorean Identities\">Pythagorean Identities<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Reciprocal_identities\" title=\"Reciprocal identities\">Reciprocal identities<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Quotient_and_cofunction_identities\" title=\"Quotient and cofunction identities\">Quotient and cofunction identities<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Sum_and_difference_formulas\" title=\"Sum and difference formulas\">Sum and difference formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Double_angle_formulas\" title=\"Double angle formulas\">Double angle formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Conclusions\" title=\"Conclusions\">Conclusions<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Frequently_asked_questions_on_Trigonometric_identities\" title=\"Frequently asked questions on Trigonometric identities\">Frequently asked questions on Trigonometric identities<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Prove_the_identity_sin%CE%B8_cot%CE%B8_cos%CE%B8\" title=\"Prove the identity: sin(\u03b8) * cot(\u03b8) = cos(\u03b8). \">Prove the identity: sin(\u03b8) * cot(\u03b8) = cos(\u03b8). <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Simplify_the_expression_sin%CE%B8_cos%CE%B82\" title=\"Simplify the expression: (sin(\u03b8) + cos(\u03b8))^2. \">Simplify the expression: (sin(\u03b8) + cos(\u03b8))^2. <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Prove_the_identity_tan%CE%B8_cot%CE%B8_1\" title=\"Prove the identity: tan(\u03b8) * cot(\u03b8) = 1. \">Prove the identity: tan(\u03b8) * cot(\u03b8) = 1. <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Find_the_value_of_cos%CF%803_using_the_unit_circle\" title=\"Find the value of cos(\u03c0\/3) using the unit circle. \">Find the value of cos(\u03c0\/3) using the unit circle. <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Prove_the_identity_cos%CE%B8_sec%CE%B8_cos%C2%B2%CE%B8\" title=\"Prove the identity: cos(\u03b8) \/ sec(\u03b8) = cos\u00b2(\u03b8). \">Prove the identity: cos(\u03b8) \/ sec(\u03b8) = cos\u00b2(\u03b8). <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Simplify_the_expression_1_-_sin%C2%B2%CE%B8_1_sin%CE%B8\" title=\"Simplify the expression: (1 &#8211; sin\u00b2\u03b8) \/ (1 + sin\u03b8). \">Simplify the expression: (1 &#8211; sin\u00b2\u03b8) \/ (1 + sin\u03b8). <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Prove_the_identity_sin90%C2%B0_-_%CE%B8_cos%CE%B8\" title=\"Prove the identity: sin(90\u00b0 &#8211; \u03b8) = cos(\u03b8). \">Prove the identity: sin(90\u00b0 &#8211; \u03b8) = cos(\u03b8). <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/#Prove_the_identity_sin%CE%B8_csc%CE%B8_1\" title=\"Prove the identity: sin(\u03b8) * csc(\u03b8) = 1. \">Prove the identity: sin(\u03b8) * csc(\u03b8) = 1. <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Trigonometric_Identities\"><\/span>Introduction to Trigonometric Identities<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Trigonometric identities are essential equations in trigonometry that link multiple trigonometric functions of an angle. These identities are essential in solving complicated trigonometric problems, analysing triangles, and simplifying formulas. In this post, we will look at popular trigonometric identities, solve them step by step, and answer commonly asked issues with thorough answers.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Pythagorean_Identities\"><\/span>Pythagorean Identities<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Pythagorean identities are essential formulas in trigonometry for right triangles.  They relate sides and angles and are widely used in calculations involving trigonometric functions.<\/p>\n<ul>\n<li>sin\u00b2(\u03b8) + cos\u00b2(\u03b8) = 1<\/li>\n<li>1 + tan\u00b2(\u03b8) = sec\u00b2(\u03b8)<\/li>\n<li>1 + cot\u00b2(\u03b8) = csc\u00b2(\u03b8)<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Reciprocal_identities\"><\/span>Reciprocal identities<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Reciprocal identities are crucial formulas in trigonometry that establish relationships between trigonometric functions and their reciprocals. These identities are useful for simplifying expressions and solving trigonometric equation<\/p>\n<ul>\n<li>csc(\u03b8) = 1 \/ sin(\u03b8)<\/li>\n<li>sec(\u03b8) = 1 \/ cos(\u03b8)<\/li>\n<li>cot(\u03b8) = 1 \/ tan(\u03b8)<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Quotient_and_cofunction_identities\"><\/span>Quotient and cofunction identities<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Quotient and cofunction identities are fundamental equations in trigonometry that connect trigonometric functions with their reciprocals and cofunctions. These identities are employed for simplifying expressions and solving trigonometric equations.<\/p>\n<ul>\n<li>tan(\u03b8) = sin(\u03b8) \/ cos(\u03b8)<\/li>\n<li>cot(\u03b8) = cos(\u03b8) \/ sin(\u03b8)<\/li>\n<\/ul>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/articles\/math-articles\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Math Articles<\/button><\/a> <a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/math-formulas\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Math Formulas<\/button><\/a> <a href=\"https:\/\/infinitylearn.com\/surge\/articles\/super-set\/\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Super Set<\/button><\/a> <a href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Trigonometry Formulas<\/button><\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sum_and_difference_formulas\"><\/span>Sum and difference formulas<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Sum and difference formulas are fundamental equations in trigonometry that provide relationships between the sum and difference of angles and trigonometric functions. These formulas are essential for expanding trigonometric expressions and solving trigonometric equations involving multiple angles.<\/p>\n<ul>\n<li>sin(\u03b1 \u00b1 \u03b2) = sin(\u03b1) * cos(\u03b2) \u00b1 cos(\u03b1) * sin(\u03b2)<\/li>\n<li>cos(\u03b1 \u00b1 \u03b2) = cos(\u03b1) * cos(\u03b2) \u2213 sin(\u03b1) * sin(\u03b2)<\/li>\n<li>tan(\u03b1 \u00b1 \u03b2) = (tan(\u03b1) \u00b1 tan(\u03b2)) \/ (1 \u2213 tan(\u03b1) * tan(\u03b2))<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Double_angle_formulas\"><\/span>Double angle formulas<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Double angle formulas are fundamental equations in trigonometry that relate trigonometric functions to their double angles. These formulas are used to simplify expressions and solve problems involving trigonometric functions.<\/p>\n<ul>\n<li>sin(2\u03b8) = 2 * sin(\u03b8) * cos(\u03b8)<\/li>\n<li>cos(2\u03b8) = cos\u00b2(\u03b8) &#8211; sin\u00b2(\u03b8) or 2 * cos\u00b2(\u03b8) \u2013 1<\/li>\n<li>tan(2\u03b8) = 2 * tan(\u03b8) \/ (1 &#8211; tan\u00b2(\u03b8))<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Conclusions\"><\/span>Conclusions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trigonometric identities are strong tools for simplifying trigonometric expressions, solving trigonometric equations, and comprehending trigonometric function connections. This article reviewed common trigonometric identities, offered solved examples with step-by-step instructions, and answered commonly asked problems with extensive answers. Students may flourish in trigonometry and its myriad real-world applications by knowing these identities and comprehending their applications.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_asked_questions_on_Trigonometric_identities\"><\/span><span class=\"TextRun SCXW6229899 BCX0\" lang=\"EN-IN\" xml:lang=\"EN-IN\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW6229899 BCX0\" data-ccp-parastyle=\"heading 2\">Frequently asked questions<\/span> on <span class=\"NormalTextRun SCXW6229899 BCX0\" data-ccp-parastyle=\"heading 2\">Trigonometric identities<\/span><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Prove_the_identity_sin%CE%B8_cot%CE%B8_cos%CE%B8\"><\/span>Prove the identity: sin(\u03b8) * cot(\u03b8) = cos(\u03b8). <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tWe can use the reciprocal identity cot(\u03b8) = cos(\u03b8) \/ sin(\u03b8). sin(\u03b8) * cot(\u03b8) = sin(\u03b8) * (cos(\u03b8) \/ sin(\u03b8)) = cos(\u03b8). \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Simplify_the_expression_sin%CE%B8_cos%CE%B82\"><\/span>Simplify the expression: (sin(\u03b8) + cos(\u03b8))^2. <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tExpand the expression using the binomial formula. (sin(\u03b8) + cos(\u03b8))^2 = sin\u00b2(\u03b8) + 2sin(\u03b8) * cos(\u03b8) + cos\u00b2(\u03b8). Using the Pythagorean identity sin\u00b2(\u03b8) + cos\u00b2(\u03b8) = 1, the expression simplifies to 1 + 2sin(\u03b8) * cos(\u03b8). \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Prove_the_identity_tan%CE%B8_cot%CE%B8_1\"><\/span>Prove the identity: tan(\u03b8) * cot(\u03b8) = 1. <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tUsing the quotient identity tan(\u03b8) = sin(\u03b8) \/ cos(\u03b8) and cot(\u03b8) = cos(\u03b8) \/ sin(\u03b8), we get: tan(\u03b8) * cot(\u03b8) = (sin(\u03b8) \/ cos(\u03b8)) * (cos(\u03b8) \/ sin(\u03b8)) = 1. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Find_the_value_of_cos%CF%803_using_the_unit_circle\"><\/span>Find the value of cos(\u03c0\/3) using the unit circle. <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn the unit circle, cos(\u03c0\/3) corresponds to the x-coordinate of the point (cos(\u03c0\/3), sin(\u03c0\/3)) which is (1\/2, \u221a3\/2). Therefore, cos(\u03c0\/3) = 1\/2. Prove the identity: cos(\u03b8) \/ sec(\u03b8) = cos\u00b2(\u03b8). \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Prove_the_identity_cos%CE%B8_sec%CE%B8_cos%C2%B2%CE%B8\"><\/span>Prove the identity: cos(\u03b8) \/ sec(\u03b8) = cos\u00b2(\u03b8). <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tUsing the reciprocal identity sec(\u03b8) = 1 \/ cos(\u03b8), we get: cos(\u03b8) \/ sec(\u03b8) = cos(\u03b8) * cos(\u03b8) = cos\u00b2(\u03b8). \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3>Simplify the expression: (1 - sin\u00b2\u03b8) \/ (1 + sin\u03b8). <\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tUsing the Pythagorean identity 1 - sin\u00b2\u03b8 = cos\u00b2\u03b8, the expression simplifies to: cos\u00b2\u03b8 \/ (1 + sin\u03b8). \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3>Prove the identity: sin(90\u00b0 - \u03b8) = cos(\u03b8). <\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tUsing the co-function identity, sin(90\u00b0 - \u03b8) = cos(\u03b8). \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Prove_the_identity_sin%CE%B8_csc%CE%B8_1\"><\/span>Prove the identity: sin(\u03b8) * csc(\u03b8) = 1. <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tUsing the reciprocal identity csc(\u03b8) = 1 \/ sin(\u03b8), we get: sin(\u03b8) * csc(\u03b8) = sin(\u03b8) * (1 \/ sin(\u03b8)) = 1. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Prove the identity: sin(\u03b8) * cot(\u03b8) = cos(\u03b8). \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"We can use the reciprocal identity cot(\u03b8) = cos(\u03b8) \/ sin(\u03b8). sin(\u03b8) * cot(\u03b8) = sin(\u03b8) * (cos(\u03b8) \/ sin(\u03b8)) = cos(\u03b8).\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Simplify the expression: (sin(\u03b8) + cos(\u03b8))^2. \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Expand the expression using the binomial formula. (sin(\u03b8) + cos(\u03b8))^2 = sin\u00b2(\u03b8) + 2sin(\u03b8) * cos(\u03b8) + cos\u00b2(\u03b8). Using the Pythagorean identity sin\u00b2(\u03b8) + cos\u00b2(\u03b8) = 1, the expression simplifies to 1 + 2sin(\u03b8) * cos(\u03b8).\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Prove the identity: tan(\u03b8) * cot(\u03b8) = 1. \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Using the quotient identity tan(\u03b8) = sin(\u03b8) \/ cos(\u03b8) and cot(\u03b8) = cos(\u03b8) \/ sin(\u03b8), we get: tan(\u03b8) * cot(\u03b8) = (sin(\u03b8) \/ cos(\u03b8)) * (cos(\u03b8) \/ sin(\u03b8)) = 1.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Find the value of cos(\u03c0\/3) using the unit circle. \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In the unit circle, cos(\u03c0\/3) corresponds to the x-coordinate of the point (cos(\u03c0\/3), sin(\u03c0\/3)) which is (1\/2, \u221a3\/2). Therefore, cos(\u03c0\/3) = 1\/2. Prove the identity: cos(\u03b8) \/ sec(\u03b8) = cos\u00b2(\u03b8).\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Prove the identity: cos(\u03b8) \/ sec(\u03b8) = cos\u00b2(\u03b8). \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Using the reciprocal identity sec(\u03b8) = 1 \/ cos(\u03b8), we get: cos(\u03b8) \/ sec(\u03b8) = cos(\u03b8) * cos(\u03b8) = cos\u00b2(\u03b8).\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Simplify the expression: (1 - sin\u00b2\u03b8) \/ (1 + sin\u03b8). \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Using the Pythagorean identity 1 - sin\u00b2\u03b8 = cos\u00b2\u03b8, the expression simplifies to: cos\u00b2\u03b8 \/ (1 + sin\u03b8).\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Prove the identity: sin(90\u00b0 - \u03b8) = cos(\u03b8). \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Using the co-function identity, sin(90\u00b0 - \u03b8) = cos(\u03b8).\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Prove the identity: sin(\u03b8) * csc(\u03b8) = 1. \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Using the reciprocal identity csc(\u03b8) = 1 \/ sin(\u03b8), we get: sin(\u03b8) * csc(\u03b8) = sin(\u03b8) * (1 \/ sin(\u03b8)) = 1.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Trigonometric Identities Trigonometric identities are essential equations in trigonometry that link multiple trigonometric functions of an angle. These [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Trigonometric identities","_yoast_wpseo_title":"All Trigonometric Identities - Complete List","_yoast_wpseo_metadesc":"Trigonometric identities are equations that relate different trigonometric functions, such as sin, cos, and tan, and are used to solve trigonometric equations.","custom_permalink":"articles\/trigonometric-identity\/"},"categories":[8442,8443],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>All Trigonometric Identities - Complete List<\/title>\n<meta name=\"description\" content=\"Trigonometric identities are equations that relate different trigonometric functions, such as sin, cos, and tan, and are used to solve trigonometric equations.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"All Trigonometric Identities - 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