Answer
See the steps.
Work Step by Step
$LHS = \cos{120} = -\dfrac{1}{2}$
$RHS = \cos^2 {60} - \sin^2 {60} = \left(\dfrac{1}{2}\right)^2 - \left(\dfrac{\sqrt{3}}{2}\right)^2$
$RHS = -\dfrac{1}{2}$
$LHS = RHS$
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