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Prove that sin [2 tan^(-1) {sqrt((1 -x)/...

Prove that `sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))`

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Let `x = cos theta, " where " `theta in [0,pi]`
`rArr y = sin [2 tan^(-1) {sqrt((1 - x)/(1 + x))}]`
`= sin [2 tan^(-1) {sqrt((1 - cos theta)/(1 + cos theta))}]`
`= sin [2 tan^(-1) {sqrt(tan^(2).(theta)/(2))}]`
`= sin [2 tan^(-1) {tan.(theta)/(2)}]`
`= sin theta`
`= sqrt(1 - x^(2))`
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