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Given that sin(2*alpha) = 4*sin(2*beta), if 5*tan(alpha - beta) = k*tan(alpha + beta), find the value of k.

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

Correct answer: 3

Solution

Writing both tangents as sine-over-cosine ratios and applying the product-to-sum identities with the constraint sin(2*alpha) = 4*sin(2*beta) yields the ratio 5*tan(alpha - beta) / tan(alpha + beta) = 3, so k = 3.

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