Using your knowledge of complex numbers, such as De Moivre's and Euler's formulae, verify the trigonometric identities for the double angle.

de Moivre's: (cos(x)+isin(x))ⁿ=cos(nx)+isin(nx) set n=2 (cos(x)+isin(x))²=cos²(x)+2isin(x)cos(x)-sin²(x), which, according to de Moivre's cos²(x)+2isin(x)cos(x)-sin²(x)=cos(2x)+isin(2x) We notice that on both the RHS and LHS we have real and complex terms, which means that the real part on one side is equal to the real part of the other, and the same stands for the imgainary bits: cos(2x)=cos²(x)-sin²(x) sin(2x)=2sin(x)cos(x) These identities are the correct ones.