Solved this equation

[Mehedi]

Use de Moivre’s theorem to test the correctness of the following trigonometric equation-

sin(2θ) ≡ 2sin(θ)cos(θ) and cos(2θ) ≡ cos2(θ)- sin2(θ)

 

[lex]

[MATH](\cos\theta + i \sin\theta)=e^{i\theta}\\ (\cos\theta + i \sin\theta)^2=(e^{i\theta})^2=e^{2i\theta}=\cos 2\theta+i\sin 2\theta \\ (\cos\theta + i \sin\theta)^2=\cos 2\theta+i\sin 2\theta[/MATH]Multiply out the left hand side, and then equate the real parts and equate the imaginary parts.