1.

Graph of `y=sin^(-1)((2x)/(1+x^2))`

Answer» ` y = sin ^(-1) ((2x)/(1+x^(2)))`
Let `x = tan theta`
`rArr theta = tan ^(1) x`
`rArr y = sin^(-1) ((2tan theta)/(1+ tan^(2) theta))`
` = sin^(-1)((2tantheta)/(sec^(2)theta)) = sin^(-1)(2sin theta costheta)`
`= sin ^(-1) (sin 2 theta) = 2 theta = 2 tan^(-1) x `
`rArr (dy)/(dx) = 2 (d)/(dx) tan 6(-1) x = (2)/(1+ x^(2))`.


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