1. ## 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?

2. 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.

$\displaystyle 2 \sin^2 5x \cos 3x$

$\displaystyle =2\left(\frac{1}{2}-\frac{1}{2} \cos 10x\right) \cos 3x$

$\displaystyle =\cos 3x - \cos 3x \cos 10x$

$\displaystyle =\cos 3x - \frac{1}{2}(\cos 13x + \cos 7x)$

3. 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

4. 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,

5. 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 . . .

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

7. Solved it.

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

8. ah, now i know what you wanted