If $$a1$$,$$a2$$,$$a3$$,…….an are in A.P with common difference d≠$$0$$, then sum of the series $$sin$$⁡dsec⁡$$a1sec$$⁡$$a2+$$$$sec$$⁡$$a2sec$$⁡$$a3+$$………$$+$$$$sec$$⁡an−$$1sec$$⁡an is

Question

If $$a1$$,$$a2$$,$$a3$$,…….an are in A.P with common difference d≠$$0$$, then sum of the  series $$sin$$⁡dsec⁡$$a1sec$$⁡$$a2+$$$$sec$$⁡$$a2sec$$⁡$$a3+$$………$$+$$$$sec$$⁡an−$$1sec$$⁡an is

Infinity Learn · Accepted Answer

As $$a1$$,$$a2$$,$$a3$$,…………an−$$1$$,an are in A.P hence $$d=a2$$−$$a1=a3$$−$$a2=$$……..$$=an$$−an−$$1sin$$⁡dsec⁡$$a1sec$$⁡$$a2+$$$$sec$$⁡$$a2sec$$⁡$$a3+$$…………….$$+$$$$sec$$⁡an−$$1sec$$⁡$$an=$$$$sin$$⁡$$a2$$−$$a1cos$$⁡$$a1cos$$⁡$$a2+$$$$sin$$⁡$$a3$$−$$a2cos$$⁡$$a2cos$$⁡$$a3+$$…………..$$+$$$$sin$$⁡an−an−$$1cos$$⁡an−$$1cos$$⁡$$an=$$$$tan$$⁡$$a2$$−$$tan$$⁡$$a1+$$$$tan$$⁡$$a3$$−$$tan$$⁡$$a2+$$…………$$+$$$$tan$$⁡an−$$tan$$⁡an−$$1=$$$$tan$$⁡an−$$tan$$⁡$$a1$$

$If a_{1}, a_{2}, a_{3}, \dots \dots . a_{n} are in A.P with common difference d \neq 0, then sum of the$
$series \sin d [\sec a_{1} \sec a_{2} + \sec a_{2} \sec a_{3} + \dots \dots \dots + \sec a_{n - 1} \sec a_{n}] is$

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If a1,a2,a3,…….an are in A.P with common difference d≠0, then sum of the series sin⁡dsec⁡a1sec⁡a2+sec⁡a2sec⁡a3+………+sec⁡an−1sec⁡an is

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$If a_{1}, a_{2}, a_{3}, \dots \dots . a_{n} are in A.P with common difference d \neq 0, then sum of the$
$series \sin d [\sec a_{1} \sec a_{2} + \sec a_{2} \sec a_{3} + \dots \dots \dots + \sec a_{n - 1} \sec a_{n}] is$