Are the given trigonometric identities correct?

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SUMMARY

The discussion centers on verifying the correctness of the trigonometric identity: (tanX + tanY) / (1 - tanXtanY) = (cotX + cotY) / (cotXcotY - 1). Participants emphasize the importance of substituting the definitions of tangent and cotangent, specifically tan = sin/cos and cot = cos/sin, to simplify the equation. The consensus is that proper substitution leads to a clearer understanding of the identity's validity. This method is essential for confirming trigonometric identities in mathematical proofs.

PREREQUISITES
  • Understanding of trigonometric functions: tangent and cotangent
  • Familiarity with trigonometric identities and equations
  • Basic algebraic manipulation skills
  • Knowledge of sine and cosine functions
NEXT STEPS
  • Practice verifying trigonometric identities using substitution methods
  • Explore advanced trigonometric identities and their proofs
  • Learn about the unit circle and its relation to trigonometric functions
  • Study the applications of trigonometric identities in calculus
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone looking to deepen their understanding of trigonometric identities and their proofs.

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Homework Statement


tanX+tan Y / 1-tanXtanY= cotX+cotY/cotXcotY-1


Homework Equations



tan= sin/cos
cot= cos/sin

The Attempt at a Solution

 
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Attempt at a solution?

Try substituting those equations into your problem. Where does that get you?
 

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