Trigonometric sum-difference formula for absolute values

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SUMMARY

The discussion focuses on deriving the trigonometric sum-difference formulas for the absolute values of sine and cosine functions, specifically sin|x + y| and cos|x + y|. Participants emphasize utilizing the even and odd properties of these functions to simplify the expressions by removing the absolute value bars. The consensus is that by applying standard sum-difference formulas after adjusting for the absolute values, one can effectively express these trigonometric identities.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Familiarity with even and odd functions in mathematics
  • Knowledge of sum-difference formulas for sine and cosine
  • Basic algebraic manipulation skills
NEXT STEPS
  • Research the even and odd properties of trigonometric functions
  • Study the standard sum-difference formulas for sine and cosine
  • Explore examples of manipulating absolute values in trigonometric identities
  • Investigate advanced applications of trigonometric identities in calculus
USEFUL FOR

Mathematics students, educators, and anyone interested in advanced trigonometric identities and their applications in various fields such as physics and engineering.

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sin|x + y| = ?
cos|x + y| = ?

Is there any formula for these?
 
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You can use the even/oddness of the functions to remove the abs bars or shift it to a constant outside, then apply the normal sum-difference formulas.
 

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