[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.
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