Question

Решите уравнение: 1-cos 2x = 2 sin x

Answer 1

$1-Cos2x=2Sinx\\\\1-(1-2Sin^{2}x)=2Sinx\\\\1-1+2Sin^{2}x-2Sinx=0\\\\2Sin^{2}x-2Sinx=0\\\\2Sinx(Sinx-1)=0\\\\1)Sinx=0\\\\x=\pi n,n\in Z\\\\2)Sinx-1=0\\\\Sinx=1\\\\x=\frac{\pi }{2} +2\pi n,n\in Z$