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Find the fundamental period of the function (sin x + sin 5x)/(cos x + cos 5x).

1. pi/3
2. pi/2
3. pi
4. 2*pi

Correct answer: pi/3

Solution

Numerator = 2 sin 3x cos 2x, denominator = 2 cos 3x cos 2x; the cos 2x cancels, leaving tan 3x. The period of tan(3x) is pi/3, which is the fundamental period of the expression.

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