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Show that sin(A - B)/(cos A cos B) + sin(B - C)/(cos B cos C) + sin(C - A)/(cos C cos A) = 0.

1. True (identity holds; each term reduces to a difference of tangents that telescopes to 0)
2. Equal to tan A + tan B + tan C
3. Equal to 1
4. Equal to tan A tan B tan C

Correct answer: True (identity holds; each term reduces to a difference of tangents that telescopes to 0)

Solution

Each fraction simplifies to a difference of tangents, and the three differences cancel, giving 0.

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