Question

If $\cos (A+B)=\frac{1}{2}=\sin (A-B)$, find $A\&B$ if $A\&B$ are acute angle.

Answer 1

$\cos (A+B)=\frac{1}{2}$

$\cos (A+B)=\cos {60}^{\circ }$

$\Rightarrow A+B={60}^{\circ }$ ............ (1)

$\sin (A-B)=\frac{1}{2}$

$\sin (A-B)=\sin {30}^{\circ }$

$\Rightarrow A-B={30}^{\circ }$ ............ (2)

Adding (1) and (2) , we get,

$2A={90}^{\circ }$

$A={45}^{\circ }$

From (1),

$B=60-A$

$=60-45$

$={15}^{\circ }$