Решите уравнение:

1) Sin 4x Cos2x = Sin 2x Cos 4x

2) Cos 2x - Sin x = 0

3) Cos (0,5 п-2x) + Sin x = 0

1) sin4xcos2s-sin2xcos4x=0

sin (4x-2x) = 0⇒sin2x=0⇒2x=πn⇒x=πn/2

2) 1-2sin²x-sinx=0

2sin²x+sinx-1=0

sinx=a⇒2a²+a-1=0

D=1+8=9

a1 = (-1-3) / 4=-1⇒sinx=-1⇒x=-π/2+2πn

a2 = (-1+3) / 4=1/2⇒sinx=1/2⇒x = (-1) ^n * π/6+πn

3) sin2x+sinx=0

2sinxcosx+sinx=0

sinx (2cosx+1) = 0

sinx=0⇒x=πn

cosx=-1/2⇒x=+-2π/3+2πn