Formula for sin(A+B)

Introduction

What is the formula for sin(A+B)?
Is sin(A+B)=sin A + sin B?
This applet shows the formula for sin(A+B) and cos(A+B).

How to use the applet

Change angles A and B by pressing "+" and "-" buttons.
The lengths of three arrows appear by checking "Character" box.
You will understand the green arrow is the sum of the red arrow and the blue arrow. That indicates the formula for sin(A+B).

Applet

Sum and Difference Formulas

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