If `y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")),` prove that `siny=tan^2x/2`

Explanation

To prove that \( \sin y = \tan^2 \frac{x}{2} \) given \( y = \cot^{-1}(\sqrt{\cos x}) - \tan^{-1}(\sqrt{\cos x}) \), we can follow these steps:

### Step 1: Rewrite \( y \)
We start with the expression for \( y \):
\[ y = \cot^{-1}(\sqrt{\cos x}) - \tan^{-1}(\sqrt{\cos x}) \]

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