Question

If $\tan (A+B)=\sqrt{3}$ and $\tan (A-B)=\frac{1}{\sqrt{3}}$ find $A$ and $B$. A and B are acute angles. Then A+B in degrees

Answer 1

Given $\tan (A+B)=\sqrt{3}⟹A+B={60}^{\circ }\cdots \left(1\right)$

$\tan (A-B)=\frac{1}{\sqrt{3}}⟹A-B={30}^{\circ }\cdots \left(2\right)$

$\left(1\right)+\left(2\right)⟹2A={90}^{\circ }⟹A={45}^{\circ }$

Put $A$ value in $\left(1\right)$

$⟹B={60}^{\circ }-{45}^{\circ }={15}^{\circ }$