căn3(sin2x-sinx)-cos2x+3cosx-2=0

Đáp án:

Giải thích các bước giải:

 `\sqrt{3}(sin2x-sinx)-cos2x+3cosx-2=0`

`<=>\sqrt{3}(2sinx.cosx-sinx)-(2cos^2x-1)+3cosx-2=0`

`<=>\sqrt{3}sinx.(2cosx-1)-(2cos^2x-3cosx+1)=0`

`<=>\sqrt{3}sinx.(2cosx-1)-(2cosx-1)(cosx-1)=0`

`<=>(2cosx-1)(\sqrt{3}sinx-cosx+1)=0`

`<=>[(cosx=1/2),(\sqrt{3}/2sinx-1/2cosx=-1/2):}`

`<=>[(x=+-\pi/3+k2\pi(k\inZZ)),(sin(x-\pi/6)=-1/2):}`

`<=>[(x=+-\pi/3+k2\pi(k\inZZ)),(x=-\pi/6+k2\pi(k\inZZ)),(x=(3\pi)/2+k2\pi(k\inZZ)):}`