134
Prove that : $\sqrt{\frac{\sec A-1}{\sec A+1}} + \sqrt{\frac{\sec A+1}{\sec A-1}} = 2 \operatorname{cosec} A$
Show SolutionHide Solution↓
LHS $$\begin{aligned}& = \sqrt{\frac{\sec A-1}{\sec A+1}} + \sqrt{\frac{\sec A+1}{\sec A-1}} \\ & = \frac{(\sec A-1) + (\sec A+1)}{\sqrt{\sec^2 A-1}} \\ & = \frac{2\sec A}{\tan A} \\ & = 2 \times \frac{\cos A}{\sin A} \times \frac{1}{\cos A} \\ & = 2 \operatorname{cosec} A = \text{RHS}\end{aligned}$$