Question

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

Answer 1

`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 = pi/2`
b. tan x = 0
Unit circle -->
x = 0 and `x = pi, and x = 2pi`
Answers for `[0, 2pi]`:
`0, pi/2, pi, 2pi`

Answer 2

`x=0, pi, 2pi`

Explanation:

Factor out the `6tanx`:

`6tanx(sinx-1)=0`

`tanx=0`
`x=pi, 0, 2pi`

`sinx=1`
`x=pi/2`

Unfortunately tangent is undefined at `pi/2` so feasible solutions:
`x=0, pi, 2pi`