# How do you solve tan 4x = tan 2x?

May 8, 2018

$\rightarrow x = \frac{n \pi}{2}$ where $n \rightarrow Z$

#### Explanation:

$\rightarrow \tan 4 x = \tan 2 x$

$\rightarrow 4 x = n \pi + 2 x$

$\rightarrow 2 x = n \pi$

$\rightarrow x = \frac{n \pi}{2}$ where $n \rightarrow Z$

NOTE THAT If $\tan x = \tan \alpha$ then $x = n \pi + \alpha$ where $n \in \mathbb{Z}$

May 18, 2018

$\rightarrow \tan 4 x = \tan 2 x$

$\rightarrow \tan 4 x - \tan 2 x = 0$

$\rightarrow \frac{\tan 4 x - \tan 2 x}{1 + \tan 4 x \cdot \tan 2 x} = \frac{0}{1 + \tan 4 x \cdot \tan 2 x}$

$\rightarrow \tan \left(4 x - 2 x\right) = 0$

$\rightarrow \tan 2 x = 0$

$\rightarrow 2 x = n \pi$

$\rightarrow x = \frac{n \pi}{2}$ where $n \in \mathbb{Z}$