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If pi/2lt=xlt=(3pi)/2 and y=sin^(-1)(sin...

If `pi/2lt=xlt=(3pi)/2` and `y=sin^(-1)(sinx)` , find `(dy)/(dx)` .

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`text { We have, } y=sin ^{-1}(sin x) `
`Rightarrow y=pi-x[because sin ^{-1}(sin x)=pi-x, text { if } x in[frac{pi}{2}, frac{3 pi}{2}]] `
`Rightarrow frac{d y}{d x}=frac{d}{d x}(pi-x) `
`Rightarrow frac{d y}{d x}=0-1 `
`Rightarrow frac{d y}{d x}=-1`
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