The Double-Angle Formulas
The double angles sin(2theta) and cos(2theta) can be rewritten as sin(theta+theta) and cos(theta+theta). Applying the cosine and sine addition formulas, we find that sin(2theta)=2sin(theta)cos(theta). Also, cos(2theta)=cos2(theta) - sin2(theta), see other forms for the two derivations. These results reappear in integral calculus, when remembering them can be the difference between a right and wrong answer.