Question

If a₁,a₂,a₃,...a_n are in A.P. with common difference d, then the sum of the series sin d [cosec a₁ cosec a₂ + cosec a₂ coseca₃ +...+cosec a_n-1 cosec a_n] is :

A. sec a₁ - sec a_n

B. cosec a₁ - cosec a_n

C. cot a₁ - cot a_n

D. tan a₁ - tan a_n 

Answer 1

Option : (C)

Here,

a₁, a₂,…,a_n are in A.P. 

Then,

d = a₂-a₁ = a₃-a₂=…=a_n-a_n-1

sin d [cosec a₁ cosec a₂ + cosec a₂ coseca₃ +...+cosec a_n-1 cosec a_n]