Question

Prove that:
$\frac{\sin 2x}{1-\cos 2x}=cotx$

Answer 1

$$\begin{gathered} \mathrm{LHS}=\frac{\sin 2x}{1-\cos 2x} \\ =\frac{2\sin x\times \cos x}{2{\sin }^{2}x}\left(\because \sin 2x,1-\cos 2x=2{\sin }^{2}x\right) \\ \mathit{}=\frac{2\sin x\times \cos x}{2\sin x\times \sin x} \\ =\frac{\cos x}{\sin x} \\ =\cot x=\mathrm{RHS} \\ \mathrm{Hence}\mathrm{proved}. \end{gathered}$$