High School Transform the system of trigonometric equations

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SUMMARY

The discussion focuses on solving a system of trigonometric equations involving variables l and L. The initial step involves eliminating the arctangent functions, followed by deriving a relationship between tan l and sin L. This relationship allows for the substitution of one variable in the equations, facilitating the solution process. Participants confirm that the problem is not related to homework assignments.

PREREQUISITES
  • Understanding of trigonometric functions, specifically arctan, tan, and sin.
  • Familiarity with algebraic manipulation of equations.
  • Knowledge of solving systems of equations.
  • Basic skills in mathematical reasoning and problem-solving.
NEXT STEPS
  • Study the properties of trigonometric identities and their applications.
  • Learn techniques for solving systems of nonlinear equations.
  • Explore methods for eliminating variables in algebraic equations.
  • Review the concepts of inverse trigonometric functions and their relationships.
USEFUL FOR

Mathematicians, students studying trigonometry, and anyone interested in solving complex equations involving trigonometric functions.

Rmax
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How to extract l and L from the following system of equations:

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Please confirm that this is not a homework problem.
First step is to get rid of the arctans in the obvious way. Then taking the ratio you can get an equation relating tan l to sin L. You can use that to eliminate one of them from one of the equations.
 
haruspex said:
Please confirm that this is not a homework problem.
First step is to get rid of the arctans in the obvious way. Then taking the ratio you can get an equation relating tan l to sin L. You can use that to eliminate one of them from one of the equations.
No, it is not a homework.
 
Rmax said:
No, it is not a homework.
Ok, so can you follow the steps I posted?
 
haruspex said:
Ok, so can you follow the steps I posted?
I'll definitely try, thank you!
 

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