Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 280: 42

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: $\{90^{\circ}+180^{\circ}n, ~60^{\circ}+360^{\circ}n, ~300^{\circ}+360^{\circ}n\}$

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