Question

How do you solve `2 cos 2θ = 4 - 5 cos θ`?

Answer 1

Solve `2cos 2x = 4 - 5cos x`

`x = +-41.41` deg

Explanation:

Use trig identity: `cos 2x = 2cos^2 x - 1`
`2(2cos^2x - 1) + 5cos x - 4 = 0`
`4cos^2 x + 5cos x - 6 = 0.` Call cos x = y, and solve
`4y^2 + 5y - 6 = 0`.
`(4y - 3)(y + 2) = 0`

`y = 3/4` and y = 2 (rejected since > 1)

`y = cos x = 3/4`--> `x = +- 41.41` deg