Question

If$\sin (A-B)=\frac{1}{2}and\cos (A+B)=\frac{1}{2}$find A and B.

Answer 1

Assuming that A and B are acute angles,

$sin(A-B)=\frac{1}{2}⟹A-B={30}^o$ ---$\left(1\right)$

$cos(A+B)=\frac{1}{2}⟹A+B={60}^o$ ---$\left(2\right)$

$\left(1\right)+\left(2\right)$

$2A={90}^o⟹A={45}^o$

Hence $B={15}^o$