Using trigonometric identities, the possible values for x is 0° or 120°.
What are trigonometric identities?
Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
[tex]cos(2x) - cos(x) = 0\\\\2cos^{2}(x) - 1 - cos(x) = 0\ (cos(2x) = 2cos^{2}(x) - 1)\\ \\2cos^{2}(x) - cos(x)-1 = 0\\\\2cos^{2}(x) - 2cos(x) + cos(x) -1 = 0\\\\2cos(x) ( cos(x) - 1)+ 1(cos(x) - 1) = 0\\\\(2cos(x) +1)(cos(x) - 1) = 0\\\\cos(x) = -1/2\ or\ 1[/tex]
Using trigonometric table,
cos(x) = 1
x = 0°
cos(x) = -1/2
-cos(x) = 1/2
cos(π - x) = 1/2
π - x = 60°
x = π - 60° = 180° - 60° = 120°
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