Question

Solve:$\left(\frac{1-\cos x}{1+\cos x}\right)={\tan }^2\frac{x}{2}$

Answer 1

LHS$=\frac{1-\cos x}{1+\cos x}=\frac{1-\cos 2\left(\frac{x}{2}\right)}{1+\cos 2\left(\frac{x}{2}\right)}=\frac{2{\sin }^2\frac{x}{2}}{2{\cos }^2\frac{x}{2}}[\because \cos 2x=2{\cos }^{2}x-1and\cos 2x=1-2{\sin }^{2}x]={\tan }^2\frac{x}{2}$

$=$RHS