Równanie trygonometryczne

[norbi123]

Rozwiąż równanie:
\(\displaystyle{ sin2x + sinx = 2+cosx - 2cos^{2}x}\)

[jarzabek89]

\(\displaystyle{ 2sinxcosx+sinx=2+cosx-2cos^{2}x}\)
\(\displaystyle{ 2sinxcosx-cosx=2-sinx-2(1-sin^{2}x)}\)
\(\displaystyle{ cosx(2sinx-1)=2-sinx-2+2sin^{2}x}\)
\(\displaystyle{ cosx(2sinx-1)=sinx(2sinx-1)}\)
\(\displaystyle{ cosx(2sinx-1)-sinx(2sinx-1)=0}\)
\(\displaystyle{ (2sinx-1)(cosx-sinx)=0}\)