Решите: sin6x * cos6x = -1/2; sinx + sin3x = 0; sin3x - sin7x = 0.

1)sin6x*cos6x=-1/2|*2
2sin6xcos6x=-1
sin12x=-1
12x=-п/2+2пn,n€z
x=-п/24+пn/6,n€z

2)sinx+sin3x=0
2sin(x+3x/2)cos(x-3x/2)=0
2sin2xcosx=0|:2
sin2xcosx=0
sin2x=0
2x=пn,n€z
x=пn/2,n€z
cosx=0
x=п/2+пn,n€z

3)sin3x-sin7x=0
2sin(3x-7x/2)cos(3x+7x/2)=0
-2sin2xcos5x=0 |:(-2)
sin2xcos5x=0
sin2x=0
2x=пn,n€z
x=пn/2,n€z
cos5x=0
5x=п/2+пn,n€z
x=п/10+пn/5,n€z