If cos ($\alpha$ + $\beta$) = 0 then sin ($\alpha$ – $\beta$) = ?

Question

KollegeApply · Accepted Answer

cos 2$\beta$ Explanation: cos ($\alpha$ + $\beta$) = 0 $\Rightarrow$ cos ($\alpha$ + $\beta$) = cos $90^\circ$ $\Rightarrow$ $\alpha$ + $\beta$ = $90^\circ$ $\Rightarrow$ $\alpha$ = ($90^\circ$ – $\beta$) $\therefore$ ($\alpha$ – $\beta$) = ($90^\circ$ – $\beta$ – $\beta$) = ($90^\circ$ – 2$\beta$) $\Rightarrow$ sin ($\alpha$ – $\beta$) = sin ($90^\circ$ – 2$\beta$) = cos 2$\beta$

AChoose Your Answer