Question

Is LHS=RHS ?

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

Say yes or no.

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient

Answer 1

The correct option is A Yes

$\sqrt{\frac{secA+1}{secA-1}}+\sqrt{\frac{secA-1}{secA+1}}$
$=\frac{secA+1}{\sqrt{se{c}^{2}A-1}}+\frac{secA-1}{\sqrt{se{c}^{2}A-1}}$
$=\frac{2secA}{\sqrt{se{c}^{2}A-1}}$
$=\frac{2secA}{tanA}$
$=\frac{2}{sinA}$
$=2cosecA$