SOLUTION: Can you help me, please? Thank you! Prove the identity sin(x+y) - sin(x-y) = 2cos(x)sin(y)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Can you help me, please? Thank you! Prove the identity sin(x+y) - sin(x-y) = 2cos(x)sin(y)       Log On


   

Question 359828: Can you help me, please? Thank you!
Prove the identity
sin(x+y) - sin(x-y) = 2cos(x)sin(y)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We're going to use the established identities

1) sin%28A%2BB%29=sin%28A%29cos%28B%29%2Bcos%28A%29sin%28B%29

2) sin%28A-B%29=sin%28A%29cos%28B%29-cos%28A%29sin%28B%29



sin%28x%2By%29+-+sin%28x-y%29+=+2cos%28x%29sin%28y%29 Start with the given equation.


sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29+-+sin%28x-y%29+=+2cos%28x%29sin%28y%29 Use the first identity (given above) to expand sin%28x%2By%29


Use the second identity (given above) to expand sin%28x-y%29


Distribute.


Group like terms.


0%2B2cos%28x%29sin%28y%29=2cos%28x%29sin%28y%29 Combine like terms.


2cos%28x%29sin%28y%29=2cos%28x%29sin%28y%29 Simplify


So this verifies the identity.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim