Solve the equation `(sqrt(3))/2sinx-cosx=cos^2x`

Explanation

`sqrt3/2sinx=cos^2x+cosx`

`sqrt3sinx=2(cos^2x+cosx)`

`3sin^2x=4(cos^2x+cosx)^2`

`3(1-cos^2x)=4(cos^4x+2cos^3x+cos^2x)`

`4cos^4x+8cos^3x+7cos^2x-3=0`

`(cosx+1)(2cosx-1)(2cos^2x+3cosx+3)=0`

`cosx=-1,1/2`

`x=(2n+1)pi,2npi+pi/3`.