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Show that sin((n+1)A) sin((n+2)A) + cos((n+1)A) cos((n+2)A) simplifies to cos(A). Which value does the expression equal?

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

Correct answer: cos(A)

Solution

By the cosine difference identity, the expression equals cos((n+2)A - (n+1)A) = cos(A).

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