Question

Sin2x=√3sinx как решить

Answer 1

$\sin2x=\sqrt3 \sin x\\ 2\sin x \cos x =\sqrt3 \sin x\\ 2\sin x \cos x -\sqrt3 \sin x=0\\ \sin x(2\cos x-\sqrt3)=0\\\\ \sin x=0\\ x=k\pi\\\\ 2\cos x-\sqrt3=0\\ 2\cos x=\sqrt3\\ \cos x=\dfrac{\sqrt3}{2}\\ x=-\dfrac{\pi}{6}+2k\pi \vee x=\dfrac{\pi}{6}+2k\pi\\\\ \boxed{x=k \pi \vee x=-\dfrac{\pi}{6}+2k\pi\vee x=\dfrac{\pi}{6}+2k\pi,\, k\in\mathbb{Z}}$

Answer 2

2sinxcosx-√3sinx=0
sinx(2cosx-√3)=0
sinx=0⇒x=πn,n∈z
cosx=√3/2⇒x=+-π/6+2πk,k∈z