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If y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)(...

If `y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2))` , find `(dy)/(dx)` .

Text Solution

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`y=cos^(-1)((1-x^2)/(1+x^2))`

Putting `x=tantheta`

`y=cos^(-1)((1-tan^2theta)/(1+tan^2theta))`

`y=cos^(-1)(cos2theta)`

`y=2theta`

Putting value of `theta=tan^(-1)x`

`y=2(tan^(-1)x)`

Differentiating both sides w.r.t. x

`dy/dx=(d(2tan^(-1)x))/dx`

`dy/dx=2(d(tan^(-1)x))/dx`

`dy/dx=2(1/(1+x^2))`

`dy/dx=2/(1+x^2)`
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