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Simplify the expression sin((n+1)A)*sin((n-1)A) + cos((n+1)A)*cos((n-1)A).

1. cos(2A)
2. sin(2A)
3. cos(2nA)
4. 1

Correct answer: cos(2A)

Solution

The expression matches the cosine difference formula with X = (n+1)A and Y = (n-1)A, so it equals cos((n+1)A - (n-1)A) = cos(2A).

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