Question

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

Answer 1

L.H.S. $=\sqrt{\frac{1-\cos A}{1+\cos A}}$
Multiplying by $\sqrt{1+\cos A}$ in numerator and denominator
$=\sqrt{\frac{1-\cos A}{1+\cos A}}\times \sqrt{\frac{1+\cos A}{1+\cos A}}$
$=\sqrt{\frac{(1-\cos A)(1+\cos A)}{(1+\cos A)(1+\cos A)}}$
$=\sqrt{\frac{1-{\cos }^{2}A}{(1+\cos A{)}^2}}=\sqrt{\frac{{\sin }^2}{(1+\cos A{)}^2}}$
$=\frac{\sin A}{1+\cos A}=$ R.H.S.