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If pilt=xlt=2pi and y=cos^(-1)(cosx) , f...

If `pilt=xlt=2pi` and `y=cos^(-1)(cosx)` , find `(dy)/(dx)` .

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