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Evaluate sin⁴(pi/8) + sin⁴(3pi/8) + sin⁴(5pi/8) + sin⁴(7pi/8).

1. 3/2
2. 1
3. 2
4. 5/2

Correct answer: 3/2

Solution

Reducing to cosines and using sin(3pi/8) = cos(pi/8), the symmetric sum evaluates to 3/2.

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