[Euler-Fermat]

$\sin(2x) = (\sin\dfrac{x}{2})^2$
จาก$ \sin\dfrac{x}{2} = \pm \sqrt{\dfrac{1-\cos x}{2}}$
$(\sin\dfrac{x}{2})^2 = \dfrac{1-\cos x}{2}$
$\sin(2x) = (\sin\dfrac{x}{2})^2$
$\sin(2x) = \dfrac{1-\cos x}{2}$
$4\sin^2(2x) = 1-2\cos x +\cos^2 x $
$8-8\cos^2 x = 1-2\cos x +\cos^2 x $
$9\cos^2 x -2\cos x - 7 = 0$
$(9\cos x +7)(\cos x - 1) =0 $
$\cos x = \dfrac{-7}{9} , 1 $

$x = 2n\pi \pm \cos^{-1}(\dfrac{-7}{9}) , 2n\pi$