Trigonometric Deduction from Euler's Formula: Finding the Correct Relations

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Discussion Overview

The discussion centers on the derivation of trigonometric identities from Euler's formula, specifically the formulas for cosine and sine of the sum of two angles. The scope includes mathematical reasoning and verification of relationships derived from complex numbers.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant requests a demonstration of how to derive the identities for cos(a+b) and sin(a+b) using Euler's formula.
  • Another participant asks for clarification on which relations the original poster believes to be incorrect.
  • A third participant suggests using the real and imaginary parts of the product of complex exponentials (cis(a) and cis(b)) to verify the identities.
  • The original poster later acknowledges that their initial confusion stemmed from a minor mistake and confirms that their relations were correct all along.

Areas of Agreement / Disagreement

Participants do not appear to disagree on the correctness of the trigonometric identities, as the original poster ultimately confirms their accuracy after clarification.

Contextual Notes

The discussion reflects a moment of confusion regarding the derivation process, highlighting the importance of careful verification in mathematical reasoning.

Hymne
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Anybody that can show how to deduce
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
From the relations that we get from eulers formula..
Should be really simple but I think that I have got some relations wrong so I need to se the real solution.:rolleyes:
Thanks!
 
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Which relations have you got wrong?
 
Your relations are fine. Use this to verify it:

[tex]cos(a + b) = Re[cis(a)cis(b)][/tex]
[tex]sin(a + b) = Im[cis(a)cis(b)][/tex]
 
neutrino said:
Which relations have you got wrong?

Hehe it turned out to be that I had it all right I had just made a stupid misstake and was to close to detect it.
Thanks for the help, both of you.
 

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