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

1) sin6x*cos6x=-1/2|*2

2sin6xcos6x=-1

sin12x=-1

12x=-п/2+2 пn, 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