Решите уравнения:1)2cos(2x-п/3)-1=02)7sin^2x-9sinx*cosx=-13)sin2x+cos(6x-п/3)=0

1)2cos(2x-п/3)-1=0
cos(2x-/3)=1/2
2x-/3=-/3+2k U 2x-/3=/3+2k
2x=2k U 2x=2/3+2k
x=k U x=/3+2k,kz

2)7sin^2x-9sinx*cosx=-1
7sinx-9sinxcosx+sinx+cosx=0
8sinx-9sinxcosx+cosx=0/cosx
8tgx-9tgx+1=0
tgx=t
8t-9t+1=0
D=81-32=49
t1=(9-7)/16=1/8tgx=1/8x=arctg1/8+k,kz
t2=(9+7)/16=1tgx=1x=/4+k,kz

3)sin2x+cos(6x-п/3)=0
cos(/2-2x)+cos(6x-/3)=0
2cos(2x+/12)*cos(4x-5/12)=0
cos(2x+/12)=02x+/12=/2+k2x=5/12+kx=5/24+k/2,kz
cos(4x+5/12)=04x+5/12=/2+k4x=/24+kx=/96+k/4.kz