If `u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta)` then sin u=

Options

A. `tan theta //2`
B. `tan^(2) theta//2`
C. `cot theta//2`
D. `cot^(2) theta//2`

Explanation

To solve the problem, we need to find \( \sin u \) where \( u = \cot^{-1}(\sqrt{\cos \theta}) - \tan^{-1}(\sqrt{\cos \theta}) \).

### Step-by-Step Solution:

1. **Express \( u \) in terms of \( \tan^{-1} \)**:
\[ u = \cot^{-1}(\sqrt{\cos \theta}) - \tan^{-1}(\sqrt{\cos \theta}) \]
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