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

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The discussion centers on proving the trigonometric equation cosx + cos3x + cos5x = sin6x/2sinx. Participants emphasize the importance of using trigonometric identities, particularly sum/difference and multiple-angle identities, to simplify the equation. There is a suggestion to express both sides in terms of single variables, such as using sin(5x) as sin(4x+x) for expansion. The use of complex numbers and Euler's formula is mentioned, although it's noted that these concepts are not typically covered in general trigonometry. Overall, the focus is on applying identities to facilitate the proof of the equation.
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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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