Решить уравнения.

1) (3-4sin x) (3+4 cos x) = 0

2) (tg x+3 ((tg+1) = 0

3) sin 2x=3 sin x cos (квадрат) x

4) sin 4x = sin 2x

1) (3-4sinx) (3+4cosx) = 0

sinx=3/4

x = (-1) ^k*arcsin3/4+πk

cosx=-3/4

x=±arccos (-3/4) + 2πn

2) (tgx+3) (tgx+1) = 0

tgx+3=0

tgx=-3

x=-arctg3+πn, n € Z

tgx+1=0

tgx=-1

x=arctg (-1) + πn

x=-π/4+πn, n € Z.

3) sin2x=3sinx*cos²x

2sinx*cosx-3sinx*cos²x=0

sinx*cosx (2-3cosx) = 0

sinx=0

x=πn, n € Z

cosx=0

x=π/2+πn, n € Z

cosx=2/3

x=±arccos2/3+πn, n € Z

4) sin4x-sin2x=0

2sin2x*cos2x-sin2x=0

sin2x (2cos2x-1) = 0

sin2x=0

2x=πk, k € Z

x=πk/2, k € Z

cos2x=1/2

2x=±π/3+2πn, n € Z

x=±π/6+πn, n € Z