# What are the solutions of 6 tanx sinx-6 tanx=0 in the interval ​[0,2pi]?

Apr 28, 2018

0; pi/2; pi; 2pi

#### Explanation:

6tan x.sin x - 6tan x = 0
6tan x(sin x - 1) = 0
Either factor should be zero.
a. sin x - 1 = 0 --> sin x = 1
Unit circle gives --> $x = \frac{\pi}{2}$
b. tan x = 0
Unit circle -->
x = 0 and $x = \pi , \mathmr{and} x = 2 \pi$
Answers for $\left[0 , 2 \pi\right]$:
$0 , \frac{\pi}{2} , \pi , 2 \pi$

Apr 28, 2018

$x = 0 , \pi , 2 \pi$

#### Explanation:

Factor out the $6 \tan x$:

$6 \tan x \left(\sin x - 1\right) = 0$

$\tan x = 0$
$x = \pi , 0 , 2 \pi$

$\sin x = 1$
$x = \frac{\pi}{2}$

Unfortunately tangent is undefined at $\frac{\pi}{2}$ so feasible solutions:
$x = 0 , \pi , 2 \pi$