If bn = integral cos^2(nx)/sinx dx , x ∈ 0, π/2 then

Question

If \(b_n = \int\limits^{\frac{\pi}2}_0 \frac{cos^2(nx)}{sin\,x}dx\) then

(1) \(\frac1{b_3 - b_2} , \frac1{b_4 - b_3}, \frac1 {b_5 - b_4}\) are in A.P. with common difference 2

(2) \(\frac1{b_3 - b_2} , \frac1{b_4 - b_3}, \frac1 {b_5 - b_4}\) are in A.P. with common difference -2

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

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

Answer 1

Correct option is (2) \(\frac1{b_3 - b_2} , \frac1{b_4 - b_3}, \frac1 {b_5 - b_4}\) are in A.P. with common difference -2

Common difference = -2