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Question 200046
JEE Mathematics · Hard

Trigonometry: Conditional identity MCQ

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Conditional identityHardQuestion 200046

Question

If A + B + C = π (angles of a triangle), then tan A + tan B + tan C equals:
  1. A
    tan A tan B tan C
    Correct
  2. B
    sin A sin B sin C
  3. C
    0
  4. D
    1

Correct answer

tan A tan B tan C

Explanation

A+B+C = π → A+B = π−C. tan(A+B) = tan(π−C) = −tan C. (tanA+tanB)/(1−tanA tanB) = −tan C. Cross-multiplying: tan A + tan B + tan C = tan A tan B tan C.

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