Question

Verify the following equalities.
$\frac{\cos {60}^{\circ }}{1+\sin {60}^{\circ }}=\frac{1}{\sec {60}^{\circ }+\tan {60}^{\circ }}$

Answer 1

$\frac{\cos 60°}{1+\sin 60°}=\frac{\frac{1}{2}}{1+\frac{\sqrt{3}}{2}}=\frac{1}{2}\times \frac{2}{2+\sqrt{3}}=\frac{1}{2+\sqrt{3}}$

$\Rightarrow \frac{1}{\sec 60°+\tan 60°}=\frac{1}{2+\sqrt{3}}=\frac{\cos 60°}{1+\sin 60°}$

Hence, the answer is verify.