Robxcp
Robxcp Robxcp
  • 25-09-2020
  • Mathematics
contestada

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

Prove that answer please , I'm stuck​

Respuesta :

Alfpfeu
Alfpfeu Alfpfeu
  • 25-09-2020

Answer:

Step-by-step explanation:

Hello,

I assume that you know that

[tex]sin(A+B)=sinAcosB+cosAsinB\\\\sin(A-B)=sinAcosB-cosAsinB[/tex]

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

[tex]cos(A+B)+isin(A+B)=e^{i(A+B)}=e^{iA}e^{iB}=(cosA+isinA)(cosB+isinB)[/tex]

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

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