Question

How do you solve `2cos^2(t)+cos(t)=1`?

Answer 1

Solve; `2cos^2 t + cos t - 1 = 0`

Explanation:

Call cos x = p, and solve the quadratic equation:
`y = v^2 + v - 1 = 0.`
Since a - b + c = 0, use shortcut: one real root is v = -1 and the other `v = -c/a = 1/2.`
Next solve the 2 basic equations: cos x = -1 and `cos x = 1/2`
a. v = cos x = -1 -> `x = pi`
b. `cos x = 1/2 -> x = +- pi/3`