The value of cos3π8cos3π8+sin3π8sin3π8=

cos3⁡π8cos⁡3π8+sin3⁡π8sin⁡3π8=cos3⁡π8sin⁡π8+sin3⁡π8cos⁡π8=cos⁡π8sin⁡π8cos2⁡π8+sin2⁡π8=12sin⁡π4=122

The value of cos3π8cos3π8+sin3π8sin3π8=

cos3⁡π8cos⁡3π8+sin3⁡π8sin⁡3π8=cos3⁡π8sin⁡π8+sin3⁡π8cos⁡π8=cos⁡π8sin⁡π8cos2⁡π8+sin2⁡π8=12sin⁡π4=122

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The value of $\cos^{3} (\frac{π}{8}) \cos (\frac{3 π}{8}) + \sin^{3} (\frac{π}{8}) \sin (\frac{3 π}{8}) =$

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1/4

$1 / \sqrt{2}$

$1 / (2 \sqrt{2})$

1/2

answer is A.

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Detailed Solution

$\begin{array}{l} \cos^{3} \frac{π}{8} \cos \frac{3 π}{8} + \sin^{3} \frac{π}{8} \sin \frac{3 π}{8} = \cos^{3} \frac{π}{8} \sin \frac{π}{8} + \sin^{3} \frac{π}{8} \cos \frac{π}{8} \\ = \cos \frac{π}{8} \sin \frac{π}{8} (\cos^{2} \frac{π}{8} + \sin^{2} \frac{π}{8}) = \frac{1}{2} \sin \frac{π}{4} = \frac{1}{2 \sqrt{2}} \end{array}$