If `cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x ,` then `sinx` is `tan^2alpha/2` (b) `cot^2alpha/2` (c) `tan^2alpha` (d) `cotalpha/2`

Explanation

To solve the equation \( \cot^{-1}(\sqrt{\cos \alpha}) - \tan^{-1}(\sqrt{\cos \alpha}) = x \) and find \( \sin x \), we can follow these steps:

### Step 1: Set up the equation
Let \( \theta = \cot^{-1}(\sqrt{\cos \alpha}) \). Then, we have:
\[ \cot \theta = \sqrt{\cos \alpha} \]
From this, we can find \( \tan \theta \):
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