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If y=sin^(-1)(sinx) , -pi/2llexlepi/2 . ...

If `y=sin^(-1)(sinx)` , `-pi/2llexlepi/2` . Then, write the value of `(dy)/(dx)` for `x in (-pi/2,pi/2)` .

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`text { We have, } y=sin ^{-1}(sin x) `
`Rightarrow y=x[because sin ^{-1}(sin x)=x, text { if } x in[-frac{pi}{2}, frac{pi}{2}]] `
`Rightarrow frac{d y}{d x}=frac{d}{d x}(x) `
`Rightarrow frac{d y}{d x}=1`
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