4cosx - 2sinx = 3 + cos2x

4cosx - 2sinx = 3 + cos2x

=> 4cosx -2sinx=3 + cos²x - sin²x

=>sin²x - 2sinx + 1 = cos²x -4cosx + 4

=>(sinx-1)²=(cosx -2)²

=> sinx-1 = cosx-2 (1)

     sinx-1=-cosx +2=>sinx + cosx=3 (loại)

(1)

=> sinx-cosx=-1

=>$\frac{1}{\sqrt[]{2} }$ sinx - $\frac{1}{\sqrt[]{2} }$ cosx = -$\frac{1}{\sqrt[]{2} }$

=)cos(π/4).sin(x) - sin(π/4).cos(x)=-$\frac{1}{\sqrt[]{2} }$

=> sin(x-π/4)=sin(-π/4)

=> x-π/4 = -π/4 + k2π =>x= k2π

      x-π/4 =-3π/4 +k2π => x=-π/2 + k2π