5.5 Multiple-Angle and Product-to-Sum Formulas

The first category involves functions of multiple angles such as sin ku and cos ku

The second category involves squares of trigonometric functions such as $\sin^2u$  

The third category involves functions of half-angles such as sin(u/2).

The fourth category involves products of trigonometric functions such as sin u cos v.

 $\sin\ 2u=2\sin u\cos u$  

 $\cos2u=\cos^2u-\sin^2u\ \ \ =2\cos^2u-1\ \ =1-2\sin^2u$  

 $\tan2u=\frac{2\tan u}{1-\tan^2u}$