Question

How do you solve `cos^2x+3cosx=-2`?

Answer 1

`x = (2k +1)pi`

Explanation:

`cos^2 x + 3cos x + 2 = 0`
Solve this quadratic equation for cos x.
Since a - b + c = 0, use shortcut. The 2 real roots are:
cos x = -1 and `cos x = -c/a = - 2` (rejected as < - 1)
Solve cos x = -1
Unit circle gives:
`x = pi + 2kpi = (2k + 1)pi`