How to Prove a Trigonometric Identity Involving x, y, and z?

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SUMMARY

The discussion focuses on proving the trigonometric identity involving variables x, y, and z, specifically demonstrating that if xy + yz + zx = 1, then (x² - 1)(y² - 1)/xy + (y² - 1)(z² - 1)/yz + (z² - 1)(x² - 1)/zx = 4. The identity utilizes trigonometric relationships, particularly cotangent identities such as cotA cotB + cotB cotC + cotC cotA = 1. Participants emphasize the importance of sharing progress to facilitate effective assistance.

PREREQUISITES
  • Understanding of trigonometric identities and their applications
  • Familiarity with algebraic manipulation of equations
  • Knowledge of cotangent functions and their relationships
  • Basic skills in mathematical proof techniques
NEXT STEPS
  • Study the derivation of cotangent identities in trigonometry
  • Practice algebraic proofs involving multiple variables
  • Explore advanced topics in trigonometric equations and identities
  • Review examples of similar trigonometric identity proofs
USEFUL FOR

Mathematics students, educators, and anyone interested in enhancing their skills in proving trigonometric identities and understanding algebraic relationships in trigonometry.

skcollins
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If xy+yz+zx=1 then prove (x^2-1)(y^2-1)/xy+(y^2-1)(z^2-1)/yz+(z^2-1)(x^2-1)/zx=4 with trigonometric identities such as cotAcotB+cotBcotC+cotCcotA=1
 
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Hello skcollins and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

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