If bn = ∫(cos^2nx)/(sin x) dx, n ∈ N, then (A) b3 - b2, b4 - b3, b5 - b4 are in an A.P. with common difference - 2

Question

If b_n = \(\int\limits_0^{\pi/2}\) (cos²nx)/(sin x) dx, n ∈ N, then 

(A) b₃ - b₂, b₄ - b₃, b₅ - b₄ are in an A.P. with common difference - 2

(B) 1/(b₃ - b₂), 1/(b₄ + b₃), 1/(b₅ - b₄) are in an A.P. with common difference - 2

(C) b₃ - b₂, b₄ - b₃, b₅ - b₄ are in a G.P.

(D) 1/(b₃ - b₂), 1/(b₄ - b₃), 1/(b₅ - b₄) are in an A.P. with common difference - 2

Answer 1

Correct option is (D) 1/(b₃ - b₂), 1/(b₄ - b₃), 1/(b₅ - b₄) are in an A.P. with common difference - 2

 1/(b₃ - b₂), 1/(b₄ - b₃), 1/(b₅ - b₄) are in an A.P. with common difference - 2