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If x in (0,pi//2), then the function f(x...

If `x in (0,pi//2)`, then the function `f(x)= x sin x +cosx +cos^(2)x` is

A

increasing

B

decreasing

C

neither increasing nor decreasing

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
Given `f(x)=kx sin x+cos x +cos^(2)x`
`:.f'(x)=sin x+x cos x-sinx -2cos x sinx`
`=cos x(x-2 sinx)`
Hence `x to 0` to `pi` then `f'(x)lt0`
i.e., `f(x)` is a decreasing function.
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