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Simplify the expression [sin((n+1)A) + 2*sin(nA) + sin((n-1)A)] / [cos((n-1)A) - cos((n+1)A)].

1. cot(A/2)
2. tan(A/2)
3. cot(nA)
4. tan(nA)

Correct answer: cot(A/2)

Solution

The numerator becomes 2*sin(nA)*(1 + cos A) and the denominator 2*sin(nA)*sin A, whose ratio is (1 + cos A)/sin A = cot(A/2).

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