Choose the correct answer The value of `int0pi/2log((4+3sinx)/(4+3cosx))dx` (A) 2 (B) `3/4` (C) 0 (D) -2

Explanation

`0`


`text { Let } I=int_{0}^{frac{pi}{2}} log (frac{4+3 sin x}{4+3 cos x}) d x ldots ldots(1) . `

`=int_{0}^{frac{pi}{2}} log [frac{4+3 sin (frac{pi}{2}-x)}{4+3 cos (frac{pi}{2}-x)}] d x `

`=int_{0}^{frac{pi}{2}} log (frac{4+3 cos x}{4+3 sin x}) d x ldots ldots(2) .`


Adding (1) and (2)

`2 I=int_{0}^{frac{x}{2}}[log (frac{4+3 sin x}{4+3 cos x})+log (frac{4+3 cos x}{4+3 sin x})] d x`

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