Question

Prove that : $\tan 2x=\frac{2\tan x}{1-{\tan }^{2}x}$

Answer 1

$\tan \left(2x\right)=\frac{2\tan \left(x\right)}{1-{\tan }^{2}x}LHS=tan\left\{\right(2x)=\tan (x+x)=\frac{\tan \left(x\right)+\tan \left(x\right)}{1-\tan \left(x\right)\tan \left(x\right)}=\frac{2\tan \left(x\right)}{1-{\tan }^{2}x}=RHS$