If `cosec theta- cot theta=1/2, 0 < theta < pi/2` then `cos theta=` `a.5/3, b. 3/5, c.-3/5, d. -5/3`

Explanation

To solve the equation \( \csc \theta - \cot \theta = \frac{1}{2} \) for \( \cos \theta \), we can follow these steps:

### Step 1: Rewrite the equation in terms of sine and cosine
We know that:
\[ \csc \theta = \frac{1}{\sin \theta} \quad \text{and} \quad \cot \theta = \frac{\cos \theta}{\sin \theta} \]
Substituting these into the equation gives:
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