1.

Differntiate the following functions by proper substitution.cos^(-1)((1-t^2)/(1+t^2))

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SOLUTION :`y=COS^(-1)((1-t^2)/(1+t^2))`[PUT`t=tantheta`
`cos^(-1)FRAC(1-tan^2thet)(1+tan^2theta)`
`=cos^(-1)cos2theta=2theta=2tan^(-1)t`
`thereforedy/dx=2/(1+t^2)`


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