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

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Correct option is A

We have,cos2⁡π3−x−cos2⁡π3+x=cos⁡π3−x+cos⁡π3+xcos⁡π3−x−cos⁡π3+x=2cos⁡π3cos⁡x×2sin⁡π3sin⁡x=32sin⁡2x≤32 for all x

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The maximum value of cos2⁡π3−x−cos2⁡π3+xis

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