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If pi/2 < x < 0 andy=tan^(-1)sqrt((1-cos...

If `pi/2 < x < 0` and`y=tan^(-1)sqrt((1-cos2x)/(1+cos2x))` . find `(dy)/(dx)`

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