Question

If $\cos$$(\alpha +\beta )=0$, then $\sin$$(\alpha -\beta )$ can be reduced to:

• A. $\cos$ $\beta$
• B. $\cos$ $2\beta$
• C. $\sin$ $\alpha$
• D. $\sin$ $2\alpha$

Answer 1

The correct option is B $\cos$ $2\beta$

$\cos (\alpha +\beta )=0$

$\Rightarrow \alpha +\beta =90°$

$\Rightarrow \alpha =90°-\beta$

$\Rightarrow \sin (\alpha -\beta )=\sin (90°-\beta -\beta )$

$=\sin (90°-2\beta )$

$=\cos 2\beta$

Hence, the answer is $\cos 2\beta .$