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Let A = cos(pi/9)*cos(4pi/9)*cos(16pi/9) and B = cos(2pi/9)*cos(8pi/9)*cos(32pi/9). Find the value of |1/(16*A*B)|.

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

Correct answer: 4

Solution

Reducing angles modulo 2pi, both A and B have magnitude 1/8, so 16*A*B has magnitude 16*(1/8)*(1/8) = 1/4, and its reciprocal magnitude is 4.

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