<p>If <span style="color: red;">cot</span> (α + β) = 0, then sin (α + 2β) = ?</p>
Step-by-Step Solution
Key Concept: Use the condition cot(α + β) = 0 to find a relationship between α and β, then substitute into sin(α + 2β).
<p><strong>Step 1:</strong> Since cot(α + β) = 0, we have α + β = π/2 + nπ, which gives β = π/2 - α + nπ</p><p><strong>Step 2:</strong> Then α + 2β = α + 2(π/2 - α + nπ) = α + π - 2α + 2nπ = π - α + 2nπ</p><p><strong>Step 3:</strong> Therefore, sin(α + 2β) = sin(π - α + 2nπ) = sin(π - α) = sin α</p><p>∴ Answer is (a).</p>
Correct Answer: a