If , prove that .
If $\tan^{-1}\left(\frac{\sqrt{1+x^2} - \sqrt{1-x^2}}{\sqrt{1+x^2} + \sqrt{1-x^2}}\right) = \alpha$, prove that $\sin 2\alpha = x^2$.
Given: $\tan^{-1}\left(\frac{\sqrt{1+x^2} - \sqrt{1-x^2}}{\sqrt{1+x^2} + \sqrt{1-x^2}}\right) = \alpha$
To show: $\sin 2\alpha = x^2$
Answer
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From ISC 2026 Mathematics Paper 1, question 8(i).