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Question

If 1+cosx f(x)dx=23(1+cosx)3/2+c, then f(x) equals

A
cosx
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B
sinx
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C
tanx
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D
1
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Solution

The correct option is B sinx
1+cosxf(x)dx=23(1+cosx)3/2+c
Differentiating both sides w.r.t. x,
ddx(1+cosxf(x)dx)=ddx(23(1+cosx)3/2+c)

1+cosxf(x)=23×32(1+cosx)1/2(sinx)+0

1+cosxf(x)=sinx1+cosx

f(x)=sinx

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