Question

All solutions on interval (0, 2pi)
sin2x=2sinx

Answer 1

\(2\sin x\cos x-\sin x=0\)
\(\sin x(2\cos x-1)=0\)
\(\sin x=0\Rightarrow x=\pi\)
\(\cos x=1/2\Rightarrow x=\pi/3,4\pi/3\).

Answer 2

Sorry I made a mistake

Answer 3

\(2\sin x\cos x-2\sin x=0\)
\(2\sin x(\cos x-1)=0\)
\(\sin x=0\Rightarrow x=\pi\)
\(\cos x=1\)(no solution on (0,2pi)