Question

Verify the following equalities.
$\frac{\sec {30}^{\circ }+\tan {30}^{\circ }}{\sec {30}^{\circ }-\tan {30}^{\circ }}=\frac{1+\sin {30}^{\circ }}{1-\sin {30}^{\circ }}$

Answer 1

$\frac{\sec 30°+\tan 30°}{\sec 30°-\tan 30°}=\frac{1+\sin 30°}{1-\sin 30°}$

$\Rightarrow L.H.S=\frac{\sec 30°+\tan 30°}{\sec 30°-\tan 30°}=\frac{\frac{1}{\cos 30°}+\frac{\sin 30°}{\cos 30°}}{\frac{1}{\cos 30°}-\frac{\sin 30°}{\cos 30°}}$

$=\frac{(1+\sin 30°)}{\cos 30°}\times \frac{\cos 30°}{1-\sin 30°}$

$=\frac{1+\sin 30°}{1-\sin 30°}=R.H.S$

Hence, the answer is verify.