Question

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

A. sec a₁ - sec a_n

B. cosec a₁ - cosec a_n

C. cot a₁ - cot a_n

D tan a_n - tan a₁

Answer 1

Option : (D)

Here,

a₁, a₂,…,a_n are in A.P. 

Then,

d = a₂ - a₁ = a₃ - a₂ =…= a_n- a_n-1

sin d [sec a₁ sec a₂ + sec a₂ sec a₃ + ...+ sec a_n-1 sec a_n]