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Differentiate cos^(-1)((1-x^2)/(1+x^2)),...

Differentiate `cos^(-1)((1-x^2)/(1+x^2))`, `0lt xlt1` with respect to `x`

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Verified by Experts

Given that,
`y=cos^(-1)((1-x^2)/(1+x^2))`
`0lt xlt1`
`x= tan theta`
so, `y=cos ^-1 [(1-tan^2theta)/(sec^2theta)]`
`=>y=cos^-1(cos^2 theta - sin^2 theta)`
`=>y=cos^-1(cos2theta)`
`0lt xlt1`
`=> 0lt tan theta lt1`
`=>0 lt 2theta lt pi/2`
`y=2theta`
`=>y= 2tan^-1x`
`(dy)/(dx)=2 *d/(dx) tan^-1 x`
`=2/(1+x^2)`
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