If `tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha` , then `x^2=` `sin2\ alpha` (b) `sin\ alpha` (c) `cos2\ alpha` (d) `cos\ alpha`

Explanation

To solve the given problem, we start with the equation:

\[ \tan^{-1}\left(\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right) = \alpha \]

### Step 1: Rewrite the equation
Let:
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