Can you Simplify the Trigonometric Expression: cos 4x + cos 3x/ sin4x - sin 3x?

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  • Thread starter Thread starter Cutie13
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SUMMARY

The discussion focuses on simplifying the trigonometric expression cos(4x) + cos(3x) / sin(4x) - sin(3x). The correct answer provided in the book is cot(x/2). Participants emphasize the need to expand the trigonometric functions using the sum formulas for sine and cosine, specifically sin(a+b) and cos(a+b), to rewrite cos(4x) as cos(3x+x). This approach is essential for correctly simplifying the expression.

PREREQUISITES
  • Understanding of trigonometric identities, specifically sum formulas for sine and cosine.
  • Familiarity with the concept of cotangent and its relationship to sine and cosine.
  • Basic algebra skills for manipulating trigonometric expressions.
  • Knowledge of how to factor and expand expressions in trigonometry.
NEXT STEPS
  • Study the sine and cosine sum formulas in detail.
  • Practice simplifying trigonometric expressions using cotangent identities.
  • Explore examples of factoring trigonometric functions in various contexts.
  • Learn about advanced trigonometric identities and their applications in problem-solving.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their skills in simplifying complex trigonometric expressions.

Cutie13
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cos 4x + cos 3x/ sin4x - sin 3x
Please somebody check this over!

The answer in the book is: cot (x/2)
 
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What do you mean by check this over? You've not done anything yet! Try expanding the trigonometric functions so that they end up in terms of cos(x) and sin(x).
 
cos (4x+3x)
____________
sin (4x+3x)
 
or does the x have to be fatored out also?
am i on right track
 
No. Have you come across formulae, for general a and b, for sin(a+b) and cos(a+b)? If so, try writing cos(4x) as cos(3x+x).
 

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