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Simplify sin(cot^(-1)(cos(tan^(-1)x))),0...

Simplify `sin(cot^(-1)(cos(tan^(-1)x))),0 ltxlt1`.

Text Solution

Verified by Experts

`y=sin(cot^(-1)(cos(tan^(-1)x)))`
Let `tan^(-1)x=theta`
`rArrx=tan theta`
`:.y=sin(cot^(-1)(costheta))`
`=sin(cot^(-1)(1/sqrt(1+x^2))`
Let `cot^(-1)(1/sqrt(1+x^2))=phi`
`rArrcotphi=1/sqrt(1+x^2)`
`rArry=sintheta`
`=sqrt((1+x^2)/(2+x^2))`
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