Question

Show that :
$\frac{\cos {30}^{\circ }+\sin {60}^{\circ }}{1+\sin {30}^{\circ }+\cos {60}^{\circ }}=\cos {30}^{\circ }$.

Answer 1

$LHS$:

$\frac{\cos {30}^{\circ }+\sin {60}^{\circ }}{1+\sin {30}^{\circ }+\cos {60}^{\circ }}$

$=\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}$

$LHS=\frac{\sqrt{3}}{2}$

$RHS$:

$\cos {30}^{\circ }=\frac{\sqrt{3}}{2}$

$LHS=RHS$.