Question

If $cos(\alpha +\beta )=0,$ then $sin(\alpha +2\beta )$ is equal to

• A. $sin\alpha$
  
• B. $cos2\beta$
  
• C. $cos\alpha$
  
• D. $sin2\alpha$

Answer 1

The correct option is A $sin\alpha$


Given:
$cos(\alpha +\beta )=0$
$\Rightarrow \frac{cos(\alpha +\beta )}{sin(\alpha +\beta )}=0$
$\Rightarrow cos(\alpha +\beta )=0$
$\Rightarrow \alpha +\beta =\frac{\pi }{2}$
Therefore, $sin(\alpha +2\beta )=sin(\alpha +\alpha +\beta )=sin\alpha$