Question

Prove that : $\frac{cos{30}^{\circ }+sin{60}^{\circ }}{1+cos{60}^{\circ }+sin{30}^{\circ }}=\frac{\sqrt{3}}{2}$

Answer 1

We have,
$LHS=\frac{cos{30}^{\circ }+sin{60}^{\circ }}{1+cos{60}^{\circ }+sin{30}^{\circ }}$
$=\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}$
$=\frac{2\left(\frac{\sqrt{3}}{2}\right)}{2}$
$=\frac{\sqrt{3}}{2}$