Final answer:
The solution set to the equation cos 2θ = cos θ includes all angles except 45°, 135°, 225°, and 315°.
Step-by-step explanation:
The solution set to the equation cos 2θ = cos θ can be found by first using the double angle formula for cosine: cos 2θ = 2cos^2(θ) - 1. Substituting this into the equation, we get 2cos^2(θ) - 1 = cos θ.
Now, we can simplify this equation:
2cos^2(θ) - cos θ - 1 = 0
Factoring this equation, we have (2cos θ + 1)(cos θ - 1) = 0. Therefore, the cos θ = -1/2 or cos θ = 1.
Now, we can find the angles for which these equations are true:
For cos θ = -1/2, the angle θ can be found using the inverse cosine function: θ = 120° or 240°.
For cos θ = 1, the angle θ can be found using the inverse cosine function: θ = 0°.
Therefore, the solution set to the equation cos 2θ = cos θ includes all angles except 45°, 135°, 225°, and 315°.