Finding the Final Sum of Trigonometric Functions: Cosine and Sine Formulas

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Homework Help Overview

The discussion revolves around finding the sums of trigonometric functions, specifically the finite sums of cosines and sines raised to the second power. The original poster presents a complex approach involving Euler's formula and seeks guidance on how to proceed with their calculations.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the definitions of the sums and question the use of complex numbers in the calculations. There are discussions about the Pythagorean trigonometric identity and the geometric series, with some participants suggesting different methods to approach the problem.

Discussion Status

The conversation is ongoing, with various participants offering insights and questioning the original poster's understanding of the concepts involved. Some guidance has been provided regarding the geometric series and the use of Euler's formula, but there is no clear consensus on the next steps.

Contextual Notes

Several participants note that the original poster may lack foundational knowledge about summing geometric series and the application of complex numbers in trigonometric contexts, which may hinder their progress in solving the problem.

  • #61
Physicsissuef said:
Am I right?


Yes!
 
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  • #62
D H said:
Does helping the exact same person on the exact same question with the exact same frustration level but in another forum count?

It counts double.
 
  • #63
But can you tell me please how did they simplify it?
 
  • #64
I think you should try it first. I don't see any '2' factors in the final result. So you might start with a double angle formula.
 
  • #65
\frac{cos^2x-sin^2x+cos^2nx-sin^2nx-cos^2(n+1)x+sin^2(n+1)x-sin^2x-cos^2x}{4sin^2x}

\frac{-2sin^2x+cos^2nx-sin^2nx-cos^2(n+1)x+sin^2(n+1)x}{4sin^2x}

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