Question

Prove that $\frac{1}{\sec A-1}+\frac{1}{\sec A+1}=2co\sec A\cot A$

Answer 1

LHS$=\frac{1}{\sec A-1}+\frac{1}{\sec A+1}$

$=\frac{\sec A+1+\sec A-1}{{\sec }^{2}A-1}$

$=\frac{2\sec A}{{\tan }^{2}A}$

$=2cosecA\cot A$

$=RHS$

Hence proved