Question

Prove that :
$\sqrt{\frac{1+\cos A}{1-\cos A}}=(\csc A+\cot A)$

Answer 1

$\sqrt{\frac{1+\cos A}{1-\cos A}}$

$=\sqrt{\frac{{(1+\cos A)}^2}{1-{\cos }^{2}A}}$

$=\sqrt{{\left(\frac{1+\cos A}{\sin A}\right)}^2}$

$=\frac{1+\cos A}{\sin A}$

$=\frac{1}{\sin A}+\frac{\cos A}{\sin A}$

$=\csc A+\cot A$