Search for: If f(x)=limn→∞ ∑r=0n tanx2r+1+tan3x2r+11−tan2x2r+1 then limx→0 f(x)x is equal to If f(x)=limn→∞ ∑r=0n tanx2r+1+tan3x2r+11−tan2x2r+1 then limx→0 f(x)x is equal to A1B0C-1DNone of these Fill Out the Form for Expert Academic Guidance!l Grade ---Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12 Target Exam JEENEETCBSE +91 Preferred time slot for the call ---9 am10 am11 am12 pm1 pm2 pm3 pm4 pm5 pm6 pm7 pm8pm9 pm10pm Please indicate your interest Live ClassesBooksTest SeriesSelf Learning Language ---EnglishHindiMarathiTamilTeluguMalayalam Are you a Sri Chaitanya student? NoYes Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:Let αr=x2r+1,r=0,1,2,…,n. Then, tanx2r+1+tan3x2r+11−tan2x2r+1=tanα+tan3αr1−tan2αr=tanαr1+tan2αr1−tan2αr =tanαrcos2αr=sinαrcosαrcos2αr=sin2αr−αrcosαrcos2αr=tan2αr−tanαr∴ f(x)=limn→∞ ∑r=0n tan2αr−tanαr⇒ f(x)=limn→∞ ∑r=0n tanx2r−tanx2r+1⇒ f(x)=limn→∞ tanx−tanx2n+1=tanxHence, limx→0 f(x)x=limx→0 tanxx=1 Related content CBSE Board Exam 2024 Essay on Tsunami For Students and Children Essay on Earth For Students Essay On Natural Disaster For Students in English Save Animals Slogans in Hindi, English and Other Languages IPL 2024 Retentions: Full List of Players Retained, Released and Purse CBSE Class 12 Physical Education Syllabus 2023-24 My Mother Paragraph – Paragraph on My Mother CBSE Syllabus for Class 1 to 12 Unity of Diversity Essay For Students