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cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8...

`cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4((7pi)/8)=`

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To solve the expression \( \cos^4\left(\frac{\pi}{8}\right) + \cos^4\left(\frac{3\pi}{8}\right) + \cos^4\left(\frac{5\pi}{8}\right) + \cos^4\left(\frac{7\pi}{8}\right) \), we can follow these steps: ### Step 1: Rewrite the cosines We can use the property of cosine in different quadrants: - \( \cos\left(\frac{5\pi}{8}\right) = \cos\left(\pi - \frac{3\pi}{8}\right) = -\cos\left(\frac{3\pi}{8}\right) \) - \( \cos\left(\frac{7\pi}{8}\right) = \cos\left(\pi - \frac{\pi}{8}\right) = -\cos\left(\frac{\pi}{8}\right) \) Thus, we can rewrite: ...
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