Question

Evaluate $\frac{\tan {45}^{\circ }}{\tan {30}^{\circ }+\tan {60}^{\circ }}$

Answer 1

$\frac{\tan 45°}{\tan 30°+\tan 60°}=\frac{1}{\frac{1}{\sqrt{3}}+\sqrt{3}}=\frac{\sqrt{3}}{1+3}=\frac{\sqrt{3}}{4}$

Hence, the answer is $\frac{\sqrt{3}}{4}.$