If `sin theta = (2m n)/(m^(2) + n^(2))`, find the value of `(sin theta cot theta)/(cos theta)`

Answer

To solve the problem, we need to find the value of \(\frac{\sin \theta \cot \theta}{\cos \theta}\) given that \(\sin \theta = \frac{2mn}{m^2 + n^2}\).

### Step-by-Step Solution:

1. **Write the expression**: We start with the expression we need to evaluate:
\[ \frac{\sin \theta \cot \theta}{\cos \theta} \]

2. **Substitute cotangent**: Recall that \(\cot \theta = \frac{\cos \theta}{\sin \theta}\). Substituting this into our expression gives:
\[ \frac{\sin \theta \cdot \frac{\cos \theta}{\sin \theta}}{\cos \theta} \]

3. **Simplify the expression**: The \(\sin \theta\) in the numerator and denominator cancels out:
\[ \frac{\cos \theta}{\cos \theta} \]

4. **Final simplification**: This simplifies to:
\[ 1 \]

Thus, the value of \(\frac{\sin \theta \cot \theta}{\cos \theta}\) is \(1\).