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Simplify the expression cos(45deg - A)*cos(45deg - B) - sin(45deg - A)*sin(45deg - B). Which of the following does it equal?

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

Correct answer: sin(A + B)

Solution

The expression equals cos((45-A)+(45-B)) = cos(90 - (A+B)) = sin(A+B).

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