Question 724295: Please help me prove this??? Prove the identity sin(A+B) cos B − cos(A+B) sin B = sin A
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! sin(A+B)*cos B - cos(A+B)*sin B = sin A
These problems will be a lot easier for you once you figure out that various identities are just patterns and that the variables in them are just place-holders. They can be replaced by any appropriate expression and the equation will still be true!
So when you learn that
sin(A-B) = sin(A)cos(B) - cos(A)sin(B)
look at the patterns of the A's and B's. Think of this as:
sin(something-somethingelse) = sin(something)cos(somethingelse) - cos(something)sin(somethingelse)
Once you start looking at the identities this way, you will start to notice things like the fact that the left side of your equation matches the pattern of the right side of this identity! In this case the "A" of the identity has been replaced by "A+B" and the "B" of the identity is actually a "B". So according to the left side of the identity, the left side of your equation is equal to:
sin((A+B)-B) = sin(A)
which simplifies to just
sin(A) = sin(A)
P.S. A much slower, harder way to solve this is to replace the sin(A+B) in your equation with (sin(A)cos(B) - cos(A)sin(B)) and then try to simplify it down to to just sin(A).
|
|
|
