Question

Can I please get some help :/ Prove the following identity, showing each step in your work.
sin (A + B) – sin (A – B) = 2 cos A sin B

Answer 1

You know the identity for the sum of two angles?
sin(x + y) = sin x cos y + cos x sin y

Answer 2

Oh, yea that looks familiar.

Answer 3

from the double formula:

sin (A + B) = sin A cos B + sin B cos A

and

sin (A - B) = sin A cos B - sin B cos A

if we are going to substitute these to the given equations it will give us

Sin (A+B) - Sin (A-B) = [sin A cos B + sin B cos A] - [sin A cos B - sin B cos A]

simplify:

Sin (A+B) - Sin (A-B) = sin A cos B - sin A cos B + sin B cos A + sin B cos A

Sin (A+B) - Sin (A-B) = 2 sin B cos A

Answer 4

Dang. Thanks hba :)

Answer 5

ur welcome @IloveCharlie