Question

Prove that:
$\frac{\sin 2x}{1+\cos 2x}=\tan x$

Answer 1

$$\begin{gathered} \mathrm{LHS}=\frac{\sin 2x}{1+\cos 2x} \\ =\frac{2\sin x\times \cos x}{1+2{\cos }^{2}x-1}\left[\because \sin 2x=2\sin x\times \cos x\mathrm{and}\cos 2x=2\cos {}^{2}x-1\right] \\ =\frac{2\sin x\times \cos x}{2\cos x\times \cos x} \\ =\frac{\sin x}{\cos x} \\ =\tan x=\mathrm{RHS} \\ \mathrm{Hence}\mathrm{proved}. \end{gathered}$$