Answer: tanA tanB tanC.
- A 0, assuming the angles cancel out
- B 1, treating the identity as trivial
- C tanA tanB tanC
- D π, confusing it with the angle sum
Correct answer: C. tanA tanB tanC
Explanation: If A+B+C = π, then tan(A+B+C) is undefined (tan π = 0 but formula gives tanA+tanB+tanC - tanAtanBtanC = 0 at numerator when sum is 0... Actually the identity: tanA+tanB+tanC = tanA tanB tanC when A+B+C=nπ.
Unit circle with standard angles 0, 30, 45, 60, 90 degrees; at 45 degrees the point is (cos45, sin45) = (1/sqrt2, 1/sqrt2).
Concept context
Ratios, identities, and applications in triangles