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Question
If cot (α + β) = 0, sin (α + 2β) is equal to
Options
sin α
cos 2 β
cos α
sin 2 α
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Solution
sin α
Given:
\[\cot(\alpha + \beta) = 0\]
\[ \Rightarrow \frac{\cos(\alpha + \beta)}{\sin(\alpha + \beta)} = 0\]
\[ \Rightarrow \cos(\alpha + \beta) = 0\]
\[ \Rightarrow \alpha+\beta= \frac{\pi}{2}\]
\[\text{ Therefore, }\sin\left( \alpha + 2\beta \right) = \sin \left( \alpha + \alpha + \beta \right)\]
\[ = \sin \alpha\]
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