প্রমাণ কর যে, $\sqrt{\frac{secA+1}{secA-1}}=cotA+cosecA$

Left Hand Side

$=\sqrt{\frac{secA+1}{secA-1}}$

$=\frac{\sqrt{secA+1}}{\sqrt{secA-1}}$

$=\frac{\sqrt{secA+1}}{\sqrt{secA-1}} \times \frac{\sqrt{secA+1}}{\sqrt{secA+1}}$

$=\frac{\left(\sqrt{secA+1}\right)^2}{\sqrt{(secA-1)(secA+1)}}$

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

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

$=\frac{secA+1}{\sqrt{tan^2A}}$

$=\frac{secA+1}{tanA}$

$=\frac{secA}{tanA} + \frac{1}{tanA}$

$=\frac{\frac{1}{cosA}}{\frac{sinA}{cosA}} + cotA$

$=\left(\frac{1}{cosA} \times \frac{cosA}{sinA}\right) + cotA$

$=\frac{1}{sinA} + cotA$

$=cosecA + cotA$

$=cotA+cosecA$

$=$ Right Hand Side

[ Proved ]