\sin\left(2a\right) = \sin\left(a+a\right) = \sin a \cos a+\sin a \cos a = 2\sin a \cos a\\&amp;#10;\cos\left(2a\right) = \cos\left(a+a\right) = \cos a \cos a - \sin a \sin a= \cos ^2a - \sin^2a