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Evaluate the product sin(pi/5) sin(2pi/5) sin(3pi/5) sin(4pi/5).

1. 5/16
2. 1/16
3. sqrt(5)/16
4. 1/8

Correct answer: 5/16

Solution

The product of sin(k*pi/n) for k = 1 to n-1 equals n/2^(n-1); with n = 5 this gives 5/16.

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