anonymous
  • anonymous
Verify: sin (x+y)cos(x-y)=sin(x) cos(x)+cos(y)sin(y)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
welshfella
  • welshfella
use the compound angle formula to expand the left side then simplify. I think you will be able to make use of the identity sin^2 x + cos^2 x = 1
welshfella
  • welshfella
sin(x + y) = sin x cos y + sin y cos x cos (x - y) = cos x cos y + sin x sin y
anonymous
  • anonymous
Well once it's broken down where do I go from there?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

welshfella
  • welshfella
you should get what is on the right side so proving the identity
welshfella
  • welshfella
its a bit long winded but that is the way to do it
anonymous
  • anonymous
Can u show me all the way to the answer? My brain is ready to fall outta my ears from trying to figure this out.
zepdrix
  • zepdrix
Ehhh I can maybe show you a few steps -_- let's see here....
zepdrix
  • zepdrix
\[\large\rm \color{orangered}{\sin(x + y) = \sin x \cos y + \sin y \cos x}\]\[\large\rm \color{royalblue}{\cos (x - y) = \cos x \cos y + \sin x \sin y}\]We'll apply these identities to our problem:\[\large\rm \color{orangered}{\sin(x+y)}\color{royalblue}{\cos(x-y)}\]Which will give us:\[\large\rm \color{orangered}{\left[\sin x \cos y + \sin y \cos x\right]}\color{royalblue}{\left[\cos x \cos y + \sin x \sin y\right]}\]Ok with that first step? :)
anonymous
  • anonymous
Yes I understand that!
zepdrix
  • zepdrix
So hmm.. I guess we have to FOIL from here.
zepdrix
  • zepdrix
\[\rm =\color{orangered}{\sin x \cos y}\color{royalblue}{\cos x \cos y}+\color{orangered}{\sin x \cos y}\color{royalblue}{\sin x \sin y}\\+\color{orangered}{\sin y \cos x}\color{royalblue}{\cos x \cos y}+\color{orangered}{\sin y \cos x}\color{royalblue}{\sin x \sin y}\]Which becomes this I suppose.

Looking for something else?

Not the answer you are looking for? Search for more explanations.