Question

can someone help solve cos(2x)+cos(4x)=0

x is really just theta

Answer 1

Do you know the formula: cos(2x)=2cos²x-1?
You use is to convert to a cosine of half the original angle.
So you can also use it to convert cos(4x) to something with cos(2x).

Answer 2

So you get: cos(2x) + 2cos²(2x)-1=0, or:

2cos²(2x) + cos(2x) - 1=0

This is a second degree polynomial: to see that better set cos(2x)=p:

2p² + p - 1 = 0.
Solve it, and then remember that p = cos(2x), so solve for x then...

Answer 3

what happens to the one from changing the cos(2x) since its equal to 2cos^2x-1

Answer 4

You don't have to change that one, so you get only cos(2x) everywhere in the equation.
That makes it possible to consider it as a quadratic equation, with cos(2x) as a variable.

Answer 5

So if you have 2p² + p - 1= 0, factor it as: (2p - 1)(p + 1) = 0.
This gives p = 1/2 or p = -1.
Now remember: cos(2x) = p, so we have to solve:

cos(2x) = 1/2 and cos(2x) = -1.

Try it. If you don't succeed, let me know!