The maximum value of cos 2 ( 3 - x ) - cos 2 ( 3 + x ) is

Question

The maximum value of $\cos^{2} (\frac{π}{3} - x) - \cos^{2} (\frac{π}{3} + x)$ is

Smart Achievers · Accepted Answer

(3)

$\cos^{2} (\frac{π}{3} - x) - \cos^{2} (\frac{π}{3} + x)$

$= [\cos (\frac{π}{3} - x) + \cos (\frac{π}{3} + x)] [\cos (\frac{π}{3} - x) - \cos (\frac{π}{3} + x)]$

$= (2 \cos \frac{π}{3} \cos x) (2 \sin \frac{π}{3} \sin x)$

$= \sin \frac{2 π}{3} \sin 2 x = \frac{\sqrt{3}}{2} \sin 2 x$

Hence, maximum value of the given expression is $\frac{\sqrt{3}}{2} .$

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