All I assume is that you know Euler formula. The double-angle formulas are proved from the sum formulas by putting v. Sin 2 1 cos 2.
Cos 2 1 cos 2.
Cos 2th 1 - 2sin 2 th Equation 1 cos 2th 2cos 2 th - 1 Equation 2 Note that the equations above are identities meaning the equations are true for any value of the variable th. Sina v sina a sin 2a. Sin2th sinthcosth costhsinth. For easy reference the cosines of double angle are listed below.