Sum to product and product to sum

[Jerrybob]

Hello, I'm new here and this website seems very nice!
I've been having trouble with two problems.

Cos11x + Cos 13x - express as a product The formula I know is cosa + cosb = 2cos a+b/2 cos a-b/2
=2cos 11x+13x/2 cos 11x-13x/2
=2cos12x Cos-x ?? This is the part I have trouble with this one, just how to write it. Is the last part written as cos-x or another way?

The other problem I have is with: 3sin2xcos5x write product as sum formula is 1/2{sin(A+B) + sin(A-B)
= 3(1/2){sin(2x+5x) + sin(2x-5x)
=3/2(sin7x + sin -3x) ??

The negatives in both problems is really what is throwing me off.
Any help is greatly appreciated!

 

[royhaas]

The cosine is an even function; the sine is an odd function.

 

[Deleted member 4993]

Hello, I'm new here and this website seems very nice!
I've been having trouble with two problems.

Cos11x + Cos 13x - express as a product The formula I know is cosa + cosb = 2cos a+b/2 cos a-b/2
=2cos 11x+13x/2 cos 11x-13x/2
=2cos12x Cos-x ?? This is the part I have trouble with this one, just how to write it. Is the last part written as cos-x or another way?

since cos(-x) = cos(x)

we can write

= 2*cos(12x)*cos(x)

The other problem I have is with: 3sin2xcos5x write product as sum formula is 1/2{sin(A+B) + sin(A-B)
= 3(1/2){sin(2x+5x) + sin(2x-5x)
=3/2(sin7x + sin -3x) ??

since sin(-x) = - sin(x)

we can write

= 3/2 * [sin(7x) - sin(3x)]



The negatives in both problems is really what is throwing me off.
Any help is greatly appreciated!