Question

Tanx=(-2sqrt3/3)sinx 0<x<2pi What are all possible solutions?

Answer 1

Solve `tan x = ((-2sqrt3)/3)sin x`

Ans: `0, pi, 2pi, (+- 5pi)/6`

Explanation:

`sin x/(cos x) = ((-2sqrt3)/3)sin x`
`sin x + ((2sqrt3)/3)sin x.cos x = 0`

`sin x(1 + ((2sqrt3)/3)cos x) = 0`
a. sin x = 0 --> x = 0; `x = pi`; and `x = 2pi`
b.`(2sqrt3/3)cos x = -1` --> `cos x = -3/(2sqrt3) = - sqrt3/2` -->
`x = +- 5pi/6`.

Answer 2

The correct answer { `0,(5pi)/6,pi,(7pi)/6`}

Explanation:

I don't know why.