Question

If a₁,a_2,....,a_n are in AP with common difference d, then the sum of the following series is sind(cosec a₁. cosec a₂ + cosec a₃ + .... + cosec a_{n - 1} coseca_n)

(a) sec a₁ - sec a_n

(b) cot a₁ - cot a_n

(c)  tan a₁ - tan a_n

(d)  cosec a₁ - cosec a_n

Answer 1

Correct option  (b) cot a₁ - cot a_n

Given d = a₂ - a₁ = a₃ - a₂ = ... = a_n -a_n -1 Therefore,

 sind{cosec a₁cosec a₂ + ...+  cosec a_{n - 1}cosec a_n}