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Evaluate the product sin 12° · sin 24° · sin 48° · sin 84°.

1. cos 20° · cos 40° · cos 60° · cos 80°
2. sin 20° · sin 40° · sin 60° · sin 80°
3. 3/15
4. None of these

Correct answer: cos 20° · cos 40° · cos 60° · cos 80°

Solution

sin12 sin24 sin48 sin84 = 1/16 numerically. The product cos20 cos40 cos60 cos80 also equals 1/16, while sin20 sin40 sin60 sin80 = 3/16. Hence the equal expression is cos20 cos40 cos60 cos80.

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