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If A, B and C are the angles of a triangle, which of these statements is FALSE?

Competition practiceTrigonometry
  • Asin(A + B) = sinC
  • Bcot(A + B) = cotC
  • Ccos(A + B) = −cosC
  • Dtan(A + B) = −tanC

Step-by-Step Solution

In a triangle A + B = 180° − C. The sine of a supplement is unchanged, but the cosine, tangent and cotangent all flip sign, so cot(A + B) = −cotC, not cotC. Check with A = B = C = 60°: cot120° = −0.577 while cot60° = +0.577.
Answer: B) cot(A + B) = cotC

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