Question

How do you solve `cos(2theta)+cos(theta)=0`?

Answer 1

Use trig identity: `cos 2a = 2cos^2 a - 1.`

`2cos^2 x + cos x - 1 = 0.`

Call cos x = t, solve the quadratic equation: y = 2t^2 + t - 1 = 0

Since a - b + c = 0, use shortcut. One real root is t = -1 and the other is `(-c/a = 1/2.)`

a. cos x = t = -1 --> `x = pi`

b. `cos x = t = 1/2 --> x = +- pi/3`