## sarm22 2 years ago can someone help solve cos(2x)+cos(4x)=0 x is really just theta

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1. ZeHanz

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).

2. ZeHanz

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...

3. sarm22

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

4. ZeHanz

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.

5. ZeHanz

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!