Question

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

Answer 1

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