Answer
The solution set is:
$\{90^{\circ}+180^{\circ}n, ~60^{\circ}+360^{\circ}n, ~300^{\circ}+360^{\circ}n\}$
Work Step by Step
$cos~\theta-1= cos~2\theta$
$cos~\theta-1= 2~cos^2\theta-1$
$cos~\theta= 2~cos^2\theta$
$cos~\theta = 0~~$ or $~~cos~\theta = \frac{1}{2}$
$\theta = 90^{\circ}+180^{\circ}n$
$\theta = 60^{\circ}+360^{\circ}n$
$\theta = 300^{\circ}+360^{\circ}n$
The solution set is:
$\{90^{\circ}+180^{\circ}n, ~60^{\circ}+360^{\circ}n, ~300^{\circ}+360^{\circ}n\}$
