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Which of the following trigonometric identities is correct?

1. cos(A + B) + sin(A - B) = 2*sin(45deg + A)*cos(45deg + B)
2. (sin 2A + sin 2B)/(sin 2A - sin 2B) = tan(A + B)/tan(A - B)
3. (cos 2B + cos 2A)/(cos 2B - cos 2A) = cot(A + B)*cot(A - B)
4. all of these

Correct answer: all of these

Solution

All four classic identities reduce to true statements via sum-to-product/product-to-sum transformations, so all of them hold.

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