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Question

If y=sin1 (cos x), where x(0, 2π), then the value of dydx is

A
1, if 0<x<π
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B
1, if π<x<2π
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C
1, if 0<x<π
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D
1, if π<x<2π
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Solution

The correct option is B 1, if π<x<2π
We have,sin1(cos x)=π2cos1(cos x) =(π2x, if 0<x<ππ2(2πx), if π<x<2π =(π2x, if 0<x<πx3π2, if π<x<2πClearly, it is not differentiable at x=π. Therefore,ddx(sin1(cos x)}=(1, if 0<x<π1, if π<x<2π

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