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Simplify the following expression: (cos 6x + 6cos 4x + 15cos 2x + 10)/(cos 5x + 5cos 3x + 10cos x). What does it equal?

1. cos 2x
2. 2cos x
3. cos² x
4. 1 + cos x

Correct answer: 2cos x

Solution

Using cos terms with binomial coefficients, numerator = 2^? form reduces so that the ratio simplifies to 2cos x (verified numerically, e.g. at x=0.4 the ratio = 1.8421 = 2cos0.4). The expression equals 2cos x.

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