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Prove the identity cot(alpha) + cot(60 deg + alpha) - cot(60 deg - alpha). To what does this expression simplify?

1. 3 cot(3 alpha)
2. cot(3 alpha)
3. 3 tan(3 alpha)
4. cot(alpha)/3

Correct answer: 3 cot(3 alpha)

Solution

Combining the terms over a common denominator and applying triple-angle formulas reduces the expression to 3 cot(3 alpha).

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