Book demonstration about trigonometric relations

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SUMMARY

The forum discussion centers on the interpretation of trigonometric identities, specifically addressing a confusion regarding the use of sine versus cosine in a given equation. Participants clarify that the author’s approach to proving the identity involves taking the absolute value of both sides, which validates their statements. The discussion emphasizes the commutative property of multiplication, asserting that the order of terms does not affect the outcome. This highlights the importance of understanding fundamental trigonometric principles in mathematical proofs.

PREREQUISITES
  • Understanding of basic trigonometric identities
  • Familiarity with absolute value concepts in mathematics
  • Knowledge of the commutative property of multiplication
  • Ability to interpret mathematical proofs and equations
NEXT STEPS
  • Study the derivation of trigonometric identities in detail
  • Learn about the properties of absolute values in mathematical proofs
  • Explore the commutative property and its applications in algebra
  • Review examples of common trigonometric equations and their transformations
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone seeking to deepen their understanding of trigonometric relations and proofs.

Bunny-chan
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Homework Statement


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[/B]

In the equation between (3) and (2), why does the author says that
4853327b00864221b28222f8ec109261.png
? Isn't the trigonometric identity actually
b1d600bf2773406fb9443fa8e18b6fac.png
?

2. Homework Equations

The Attempt at a Solution

 

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You are right, but that doesn't mean that what they say is wrong. In fact it proves that their statements are correct. They want to prove something about the absolute value, so they took the absolute value of both sides.
 
FactChecker said:
You are right, but that doesn't mean that what they say is wrong. In fact it proves that their statements are correct. They want to prove something about the absolute value, so they took the absolute value of both sides.
Sorry, I don't understand what you mean. How does it prove his statement is correct?

I wasn't wondering about the absolute values, I was confused about the fact that it should be two times the cosine, not the sine.
 
Bunny-chan said:
Sorry, I don't understand what you mean. How does it prove his statement is correct?

I wasn't wondering about the absolute values, I was confused about the fact that it should be two times the cosine, not the sine.
It's the same thing. Multiplication is commutative. They just swapped the order of the multiplication.
 
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