$\sin 2\alpha = \sqrt 3 \sin \alpha $
$ \to \sin {60^ \circ } = \sqrt 3 \sin 30 \Rightarrow \frac{{\sqrt 3 }}{2}$ درست
$\sin 2\alpha = 2\cos \alpha \to \sin 60 = 2 \times \cos 30$
$ \Rightarrow \frac{{\sqrt 3 }}{2} = \cancel{2} \times \frac{{\sqrt 3 }}{{\cancel{2}}} = \frac{{\sqrt 3 }}{2} = \sqrt 3 $ غلط
$\cos 2\alpha = 2\cos \alpha \to \cos 60 = 2\cos 30$
$ \Rightarrow \frac{1}{2} = 2 \times \frac{{\sqrt 3 }}{2} \Rightarrow \frac{1}{2} = \sqrt 3 $ غلط
$\sin 2\alpha = 2\sin \alpha \to \sin 60 = 2\sin 30$
$ \Rightarrow \frac{{\sqrt 3 }}{2} = 2 \times \frac{1}{2} \Rightarrow \sqrt 3 = 1$ غلط