# How do I solve sin x tan x - sin x = 0 for (0,2pi) ?

##### 1 Answer
Nov 20, 2017

$x = \frac{\pi}{4} \text{ or } x = \frac{5 \pi}{4}$

#### Explanation:

$\text{take out a "color(blue)"common factor of sinx}$

$\Rightarrow \sin x \left(\tan x - 1\right) = 0$

$\Rightarrow \sin x = 0 \to x = 0 \text{ or "2pilarrcolor(blue)"outwith interval}$

$\tan x - 1 = 0 \Rightarrow \tan x = 1$

$\Rightarrow x = \frac{\pi}{4} \text{ or } x = \left(\pi + \frac{\pi}{4}\right) = \frac{5 \pi}{4}$

$\Rightarrow x = \frac{\pi}{4} \text{or } x = \frac{5 \pi}{4} x \in \left(0 , 2 \pi\right)$