If 3π/4<α<π, then `sqrt(2cotalpha+1/(sin^2alpha))` is equal to (a) `1+cotalpha` (b) `-1-cotalpha` (c) `1-cotalpha` (d) `-1+cotalpha`

Explanation

To solve the problem, we need to evaluate the expression \( \sqrt{2 \cot \alpha + \frac{1}{\sin^2 \alpha}} \) given that \( \frac{3\pi}{4} < \alpha < \pi \).

### Step-by-step Solution:

1. **Start with the given expression**:
\[ \sqrt{2 \cot \alpha + \frac{1}{\sin^2 \alpha}} \]
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