Question

If $2\cos (A-B)=2\sin (A+B)=\sqrt{3},$ find the value of the acute angle $A$ (in degrees)

Answer 1

$2\cos (A-B)=2\sin (A+B)=\sqrt{3}:$
$\cos (A-B)=\frac{\sqrt{3}}{2}$ or $\sin (A+B)=\frac{\sqrt{3}}{2}$
$\cos (A-B)=\cos 30$ or $\sin (A+B)=\sin 60$
$A-B=30$ or $A+B=60$
Add the two equations:
$2A=90$
$A={45}^{\circ }$
Also, $A-B=30$
$45-B=30$
$B={15}^{\circ }$