Problem involving Power-Reducing Formula

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SUMMARY

The discussion centers around the application of the Power-Reducing Formula in trigonometric identities, specifically focusing on the derivation of the term 27/8. The solution involves combining fractions, where the user calculated 1/4 + 1/8 to yield 3/8, which when multiplied by 9 results in 27/8. The user’s approach differed significantly from the expected solution, leading to confusion regarding the correct application of the formula.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the Power-Reducing Formula.
  • Proficiency in arithmetic operations involving fractions.
  • Familiarity with cosine functions and their transformations.
  • Basic algebraic manipulation skills.
NEXT STEPS
  • Study the derivation and applications of the Power-Reducing Formula in trigonometry.
  • Practice arithmetic operations with fractions to improve accuracy in calculations.
  • Explore cosine function transformations and their implications in trigonometric equations.
  • Review common mistakes in trigonometric identity problems to enhance problem-solving skills.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone seeking to improve their understanding of the Power-Reducing Formula and its applications.

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Homework Statement


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Homework Equations


How in the world did they get their solution? Where did 27/8 come from?


The Attempt at a Solution


I did the arithmetic with the fractions inside before distributing the 9, and ended up getting something like -9/4 cos2x + 9/4 cos4x. Completely different from theirs.
 
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In the step above that, you have 1/4 + 1/8 = 2/8 + 1/8 = 3/8, then times 9 is 27/8
 

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