1)1/2cos2x+V3/2sin2x=cos^2x+sin^2x
1/2cos^2x-1/2sin^2x+V3sinxcosx=cos^2x+sin^2x
1,5sin^2x-V3sinxcosx+0,5cos^2x=0, делим на cos^2x
1,5tg^2x-V3tgx+0,5=0
3tg^2x-2V3tgx+1=0
y=tgx
3y^2-2V3y+1=0
(V3y-1)^2=0
V3y=1
y=1/V3=V3/3
tgx=V3/3-> x=pi/6+pi*n
2)cos^2x+sin2x-3sin^2x=0
3sin^2x-2sinxcosx-cos^2x=0, делим на cos^2x:
3tg^2x-2tgx-1=0
y=tgx
3y^2-2y-1=0
y1=-1/3
y2=1
x1=arctg(-1/3)+pi*n
x2=pi/4+pi*n
3)1+cos4x=cos2x
(cos2x)^2+(sin2x)^2+(cos2x)^2-(sin2x)^2)=cos2x
2(cos2x)^2-cos2x=0
cos2x(2cos2x-1)=0
cos2x=0->2x=2pi*n->x1=pi*n
2cos2x=1->cos2x=1/2->2x=+-pi/6+2pi*n->x2=+-pi/12+pi*n
4)sin2x/(1-cosx)=2sinx
2sinxcosx=2sinx(1-cosx)
sinxcosx=sinx-sinxcosx
2sinxcosx-sinx=0
sinx(2cosx-1)=0
sinx=0->x1=pi*n
2cosx=1->cosx=1/2->x2=+-pi/6+2pi