Trigonometric Equations: Solving 2 sin^2x - 4 cos^2x = 0 for x in [0°,360°]

[disregardthat]

Homework Statement

Hi, I wonder how to solve, and how to get the correct answer\answers to these types of problems:

2 \sin^2{x} - 4 \cos^2{x} = 0 x \in [0°,360°]

There are many answers to this. I would really like to know how the correct way to get all of them.

Homework Equations

I do not know any relevant equations for this.

The Attempt at a Solution

I have tryed to divide them with \cos^2(x) to get \tan^2(x) But it has not worked.

 

[cristo]

Well, firstly can you reduce the expression to contain only one of sinx or cosx by using the relationship sin²x+cos²x=1?

 

[disregardthat]

No, I do not know how to do it! :\

 

[HallsofIvy]

Then you need to learn algebra! Since sin²x+ cos²x= 1, cos²x= 1- sin²x. Now replace cos²x in your equation by 1- sin² x.

 

[disregardthat]

Oh, I misunderstood. Of course...

I found this equation:

\cos^2(x) = \frac{1}{3} But how do get all the answers? There are four.

If i square root bot sides, I will get two answers, (which are correct) but not all of them... How is the right way?

 

[disregardthat]

I just found out, I took the square root, and the answer must also be negative...