Question

Solve: $\tan 3A=$ $\sin {45}^{\circ }\cos {45}^{\circ }+\sin {30}^{\circ }$

Answer 1

Given:

$tan3A=sin{45}^{\circ }cos{45}^{\circ }+sin{30}^{\circ }$

$tan3A=\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}+\frac{1}{2}$

$tan3A=\frac{1}{2}+\frac{1}{2}$

$tan3A=1$

$tan3A=tan45$

$3A=45$

$A={15}^{\circ }$