
Eulers formula trouble
How do I write
2sin²5xcos3x
to a sum of cosine and/or sinusterms?
I should use Eulers formula, and control it by putting x=0 before and after I've done it.
Don't really know how to start, looked all the chapters in my book but still can't figure it out, think it's the ² term that makes me confused.
Any tip?

Hi andreynr6
I'm not sure about the Euler formula, but I can use trigonometry manipulation to write 2sin²5xcos3x as a sum of cosine terms.
$\displaystyle 2 \sin^2 5x \cos 3x$
$\displaystyle =2\left(\frac{1}{2}\frac{1}{2} \cos 10x\right) \cos 3x$
$\displaystyle =\cos 3x  \cos 3x \cos 10x$
$\displaystyle =\cos 3x  \frac{1}{2}(\cos 13x + \cos 7x)$

ah, I did something like you also, but noticed my little mistake thanks to you.
Yeah, think I skip Euler for this time :)
Thanks!
/andrey, not so good in English.....yet

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I don't know what you are apt to, but this may help . . . .
2 sin^2 (5x) cos (3x) = 16sin^2 (x) cos (x) (cos 2x  1/2)(cos 2x + cos 4x + 1/2)^2
graph below,

or this one, because it depends on what you want to obtain . . . .
2 sin^2 5x cos 3x = 8[sin^2 (5x/2)][cos^2 (5x/2)][2cos^2 (3x/2)  1]
factoring it will do . . .

how did you do the first one? I wanna know, so I can do it myself..

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Solved it.
Here's the solution, thanks to all of you.

ah, now i know what you wanted