Prove the following Trig Equations?

Question

1) tan4x - tan2x = 0 Answer: 0, pi/2, pi

2) √3cosx - sinx = 0 Answer: -4pi/3, -pi/3

I don't know how to simplify these. I ended up with tan4x = tan2x for the first question, which didn't make much sense to me.

Oh, and the domain for #1 is [0 < x < pi] and [-2pi <= x <= 0] for #2

Whoops, I messed up the title; it's supposed to be "SOLVE the following trig equations"

Answer 1

use the formula tan2x=2tanx/(1-tan^2x)

tan 4x = 2tan2x/(1-tan^2(2x)) - tan2x = 0
2tan2x - tan2x(1-tan^2(2x)) = 0
tan2x(1+tan^2(2x)) = 0
tan2x = 0 2x = 0, pi or 2pi; x= 0, pi/2 or pi
tan^2(2x) = -1 no sol.


√3cosx - sinx = 0
tanx = √3
x = pi/3 or 4pi/3 (I don't get the neg)

Answer 2

Hint: Use the double angle formula for the first question.

For the second question, put as

sqrt(3) * cos x = sin x
tan x = sqrt (3)