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If y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqr...

If `y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))`, find `(dy)/(dx)`.

Text Solution

Verified by Experts

`x=cos2theta`
`1+x=1+cos2theta=2cos^2theta`
`sqrt(1+x)=sqrt2costheta`
`1-x=1-cos2theta=2sin^2theta`
`sqrt(1-x)=sqrt2sintheta`
`y=tan^(-1)((sqrt2costheta-sqrt2sintheta)/(sqrt2costheta+sqrt2sintheta))`
`=tan^(-1)((costheta-sintheta)/(costheta+sintheta))`
`=tan^(-1)((1-tantheta)/(1+tantheta))`
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