Question

What is the formula for $\tan 2x$?

Answer 1

Write the formula for $\tan 2x$.

In the trigonometric formula $\tan \left(C+D\right)=\frac{\tan C+\tan D}{1-\tan C\tan D}$,

Put $C=x,D=x$:

$$\begin{gathered} \tan \left(x+x\right)=\frac{\tan x+\tan x}{1-\tan x\tan x} \\ \Rightarrow \tan 2x=\frac{2\tan x}{1-{\tan }^{2}x} \end{gathered}$$

Hence, the formula for $\tan 2x$ is $\frac{2\tan x}{1-{\tan }^{2}x}$.