The value of ∫ log ((4 + 3 sin x)/(4 + 3 cos x))dx, x ∈ [0, π/2] is A. 2 B. 3/4 C. 0 D. –2

Question

The value of\(\int\limits_{0}^{\pi/2} \)log\(\Big(\cfrac{4+3\,sin\text x}{4+3\,cos\,\text x}\Big)d\text x\) is

A. 2

B. 3/4

C. 0

D. –2

Answer 1

Correct option is C. 0

Use king’s property

On adding eq.(1) and (2)

y = 0