Sin2x-2*3^ (1/2) sin^2x+4cosx-4*3^ (1/2) sinx=0

sin2x-2*3^ (1/2) sin^2x+4cosx-4*3^ (1/2) sinx=0

sin2x-2sqrt3*sin^2 x+4cosx-4sqrt3*sinx=0

2sinxcosx-2sqrt3*sin^2 x+4cosx-4sqrt3*sinx=0 |:2

sinxcosx-sqrt3*sin^2 x+2cosx-2sqrt3*sinx=0

sinx (cosx-sqrt3*sinx) + 2 (cosx-sqrt3*sinx) = 0

(sinx+2) (cosx-sqrt3*sinx) = 0

sinx+2=0

sinx=-2 - не подходит, т. к. <-1

cosx-sqrt3*sinx=0 |:cosx; cosx не равен 0

1-sqrt3*tgx=0

sqrt3*tgx=1

tgx=1/sqrt3

x=p/6+pk; k принадлежит Z