Solving Tan(A) + tan(B) + tan(C)

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SUMMARY

The discussion centers on the mathematical expression Tan(A) + tan(B) + tan(C) in the context of triangle angles. It is established that this expression does not represent a solvable equation on its own. Instead, the correct formulation to explore is the identity that states if A, B, and C are the angles of a triangle, then Tan(A) + Tan(B) + Tan(C) = Tan(A) * Tan(B) * Tan(C). This identity is crucial for further exploration and proof.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent.
  • Knowledge of triangle properties and angle relationships.
  • Familiarity with mathematical proof techniques.
  • Basic algebra skills for manipulating trigonometric identities.
NEXT STEPS
  • Research the proof of the identity Tan(A) + Tan(B) + Tan(C) = Tan(A) * Tan(B) * Tan(C) for triangle angles.
  • Explore the implications of this identity in solving trigonometric equations.
  • Study the properties of tangent functions in relation to angle sums.
  • Learn about other trigonometric identities and their applications in geometry.
USEFUL FOR

Students studying trigonometry, educators teaching geometry, and anyone interested in mathematical proofs involving triangle properties.

shinnsohai
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Recently My friend gave me a question about trigo

Homework Statement



How do I Solve This?
Tan(A) + tan(B) + tan(C)

On My Own Thought
Maybe I Think That The Question Is Quite Incomplete




2. The attempt at a solution

Any Idea To Start The Calculation?
 
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Tan(A) + tan(B) + tan(C)
is not an equation, so has no "solution".
 
Perhaps the question was something like this?
Prove that if A, B and C are the 3 angles in a triangle,
\tan A + \tan B + \tan C = (\tan A)(\tan B)(\tan C)
 
eumyang said:
Perhaps the question was something like this?
Prove that if A, B and C are the 3 angles in a triangle,
\tan A + \tan B + \tan C = (\tan A)(\tan B)(\tan C)
If your hunch is correct, :smile: then I'm sure there will be plenty of solutions to be found by a google search.
 

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