Question

How do you solve `cos2x-cosx=0` using the double angle identity?

Answer 1

Solve cos 2x - cos x = 0

Ans: `0; 2pi; +- (2pi)/3`

Explanation:

Replace in the equation (cos 2x) by `(2cos^2 x - 1)`, then solve the quadratic equation in cos x:
`2cos^2 x - cos x - 1 = 0`.

Since (a + b + c = 0), use the Shortcut. The 2 real roots are:
cos x = 1 and `cos x = c/a = -1/2.`
a. cos x = 1 --> x = 0 and `cos x = 2pi.`
b. `cos x = -1/2` --> `x = +- (2pi)/3`