Question

How do you solve `5cos(2x)+1=3cos(2x)` and find all general solutions?

Answer 1

`pi/3 = kp`
`(5pi)/3 + kpi`

Explanation:

5cos 2x + 1 = 3cos 2x
2cos 2x = - 1
cos 2x = - 1/2
Trig table and unit circle give 2 solution arcs:
`2x = +- (2pi)/3 + 2kpi` --> `x = +- (2pi)/6 + kpi = +- pi/3 + kpi`
The arc `(5pi)/3` is co-terminal to the arc `(- pi)/3`.
General answers:
`x = pi/3 + kpi`
`x = (5pi)/3 + kpi`