How do you solve 2cos² (x) - cos (x) = 0

Step-by-step explanation:

Start by factoring the left side of 2cos² (x) - cos (x) = 0:

cos x [ 2cos x - 1 ] = 0.

Then cos x = 0 and 2cos x - 1 = 0.

Restricting ourselves to positive angles between 0 and 2π, we get from cos x = 0 the angles x = π/2 and x = 3π/2.

Rewriting 2cos x - 1 = 0, we get

2cos x = 1, or cos x = 1/2. One solution is x = π/3, in the first quadrant; the other is x = 5π/3, in the fourth quadrant.