Question

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

Prove that answer please , I'm stuck​

Answer 1

Explanation:

Hello,

I assume that you know that

`sin(A+B)=sinAcosB+cosAsinB\\\\sin(A-B)=sinAcosB-cosAsinB`

One way to retrieve them quickly is to use Euler's formula and then,

`cos(A+B)+isin(A+B)=e^(i(A+B))=e^(iA)e^(iB)=(cosA+isinA)(cosB+isinB)`

and you can replace B by -B for the second formula.

So, it comes that sin(A+B)-sin(A-B)=2cosAsinB

Hope this helps