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Prove that cos⁴(pi/8) + cos⁴(3pi/8) + cos⁴(5pi/8) + cos⁴(7pi/8) = 3/2. Which statement is correct?

1. The sum equals 3/2
2. The sum equals 1
3. The sum equals 2
4. The sum equals 3/4

Correct answer: The sum equals 3/2

Solution

Expanding each cos⁴ term and summing, the cos2x and cos4x contributions cancel, leaving 4*(3/8) = 3/2.

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