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If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(s...

If `tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha,` then prove that `x^2=sin2alpha`

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To prove that \( x^2 = \sin 2\alpha \) given that \[ \tan^{-1}\left(\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right) = \alpha, \] we will follow these steps: ...
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