Question

If $\sin (A+B)=\cos (A-B)$, then the value of $(A+B)$ is

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\frac{3\pi }{4}$
• D. $\frac{\pi }{8}$

Answer 1

The correct option is B $\frac{\pi }{2}$

$\sin (A+B)=\cos (A-B)$
$\Rightarrow \sin (A+B)=\sin [{90}^o-(A-B\left)\right]$
$\Rightarrow A+B={90}^o-A-B$
$\Rightarrow 2A={90}^o\Rightarrow A={45}^o=\frac{\pi }{4}$
If $B=0$, then $A+B=\frac{\pi }{4}$
If $B={45}^o$, then $A+B={90}^o=\frac{\pi }{2}$