Решите уравнения:

1. cos²x-sin²x = - 1

2. 2sinxcox=0

3. 1+cos6x=cos3x

1) cos (x) ^2 - sin (x) ^2 = - 1

1-sin (x) ^2 - sin (x) ^2 = - 1

2sin (x) ^2 = 2

x = (-1) ^n * p/2 + n*p

2) 2cos (x) * sin (x) = 0, значит либо sin (x) = 0, либо cos (x) = 0

sin (x) = 0 x = 0 + n*p

cos (x) = 0 x = p/2 + n*p

3) 1 + cos (6x) = cos (3x)

1 + cos (3x) ^2 - sin (3x) ^2 - cos (3x) = 0

2cos (3x) ^2 - cos (3x) = 0

2cos (3x) * (cos (3x) - 1/2) = 0

cos (3x) = 0 x = p/2 + n*p

cos (3x) = 1/2 x = p/9 + n*p/3