Proving Trig Equation: cosx + cos3x +cos5x = sin6x/2sinx

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Homework Help Overview

The discussion revolves around proving a trigonometric equation involving cosine and sine functions: cosx + cos3x + cos5x = sin6x/2sinx. The subject area is trigonometry, specifically focusing on identities and transformations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various approaches to proving the equation, including the use of trigonometric identities, complex numbers, and Euler's formula. There are suggestions to express both sides of the equation in terms of common trigonometric functions and to expand using sine addition formulas.

Discussion Status

The discussion is active, with participants providing guidance on potential methods to approach the proof. There are multiple lines of reasoning being explored, including the use of identities and transformations, but no consensus has been reached on a specific method yet.

Contextual Notes

One participant notes that certain advanced concepts, like complex numbers and Euler's formula, may not be covered in general trigonometry courses, which could affect the approaches considered by the original poster.

es801
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I am having trouble proving the following trigonometric equation:
cosx + cos3x +cos5x = sin6x/2sinx

Any help would be appreciated
 
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You'll need to show us your attempt before we can help you. I assume that you are familiar with the trigonometric identities (particularly, the sum/difference & multiple-angle identities).
 
Are you familiar with complex numbers and Euler's formula?

ehild
 
ehild said:
Are you familiar with complex numbers and Euler's formula?

ehild

They don't teach those in general trigonometry. Though that would work (as it usually does).

Since this is in terms of x, I would try to use the identity (sin(x+x))= ... to get the whole thing in terms of single variables. For example sin(5x) is really sin(4x+x) which can expand, and then sin(3x+1) expands out and so on. Then it should be easy to simplify.
 
Try to write both sides in terms of cos(3x) and cos(x), using the addition rules. (x=3x-2x, 5x=3x+2x, 6x=2*(3x) ).

ehild
 

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