What trig. identity would help solve $2 + \cos(2x) = 3\cos(x)$?

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I need help with a homework question that has me puzzled. I need to solve the following equation:

$$2 + \cos(2x) = 3\cos(x)$$

I don't see a good trig identity to apply. I tried $\cos(2x) = 2\cos^2(x) - 1$ but that did not seem to help. What would be a good identity to try instead?

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1 Answer

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You have the right trig identity. Let $u=\cos(x)$. Then, using $\cos(2x)=2\cos^2(x)-1$ we have a quadratic equation $2+2u^2-1=3u$. To finish, solve this quadratic equation and substitute back $\cos(x)$

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