If `"cot"(alpha+beta)=0,` then `"sin"(alpha+2beta)` can be (a)`-sinalpha` (b) `sinbeta` (c) `cosalpha` (d) `cosbeta`

Explanation

To solve the problem, we need to find the value of \(\sin(\alpha + 2\beta)\) given that \(\cot(\alpha + \beta) = 0\).

### Step-by-Step Solution:

1. **Understanding the Given Condition**:
We know that \(\cot(\alpha + \beta) = 0\). The cotangent function is zero when its argument is an odd multiple of \(\frac{\pi}{2}\). Therefore, we can conclude:
\[
\alpha + \beta = \frac{\pi}{2} + n\pi \quad \text{for any integer } n
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