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Find the value of cos(pi/10)*cos(2*pi/10)*cos(4*pi/10)*cos(8*pi/10)*cos(16*pi/10).

1. sqrt(10 + 2*sqrt(5))/64
2. -cos(pi/10)/16
3. cos(pi/10)/16
4. -sqrt(10 + 2*sqrt(5))/16

Correct answer: -cos(pi/10)/16

Solution

The first four cosines form a doubling chain summable to sin(16t)/(16 sin t); multiplying by cos(16pi/10) and simplifying gives -cos(pi/10)/16.

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