Question

Show that ${\displaystyle \sqrt{\frac{1-\cos A}{1+\cos A}}=\frac{\sin A}{1+\cos A}}$

Answer 1

${\displaystyle L.H.S=\sqrt{\frac{1-\cos A}{1+\cos A}}}$

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

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

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

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

= R.H.S