The range of cos(x+π6)cos(x−π6) is

cos2x−sin2(π6)=cos2x−14 0≤cos2x≤1 0−14≤cos2x−14≤1−14 −14≤cos2x≤34

The range of cos(x+π6)cos(x−π6) is

cos2x−sin2(π6)=cos2x−14 0≤cos2x≤1 0−14≤cos2x−14≤1−14 −14≤cos2x≤34

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The range of $\cos (x + \frac{π}{6}) \cos (x - \frac{π}{6})$ is

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[- \frac{3}{4}, \frac{3}{4}]

[- \frac{1}{4}, \frac{3}{4}]

[- \frac{1}{4}, \frac{1}{4}]

[- \frac{1}{2}, \frac{1}{2}]

answer is C.

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Detailed Solution

\cos^{2} x - \sin^{2} (\frac{π}{6}) = \cos^{2} x - \frac{1}{4}

$0 \leq \cos^{2} x \leq 1$

$0 - \frac{1}{4} \leq \cos^{2} x - \frac{1}{4} \leq 1 - \frac{1}{4}$

$- \frac{1}{4} \leq \cos^{2} x \leq \frac{3}{4}$

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The range of cos(x+π6)cos(x−π6) is

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The range of $\cos (x + \frac{π}{6}) \cos (x - \frac{π}{6})$ is