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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 these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=x sin x+cosx+cos^(2)x`
`therefore" "f'(x)=sinx+x cos x-sinx-2cosx sinx`
`=cosx(x-2 sinx)`
For `x in (0,pi//2), xlt2 sinx.`
`therefore" "f'(x)lt0`
`"i.e., f(x) is decreasing function."`
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