1) sinx(sinx-1)=0, sin x =0, x=, sinx =1, x=2πk
2) cosx(√3sinx+cosx)=0, cos x =0, x=π/2+πk; 2sin(x+π/6)=0, x = -π/6+πk
Пошаговое объяснение:
3) cos3x+cos5x=0
2cos4xcosx=0
cos4x=0, 4x = π/2+πk, x=π/8 + πk/4
cosx =0 x=π/2+πk
4) sin3x+sinx=sin2x
2sinxcos2x=sin2x=2sinxcosx
sin x=0, x=πk
cos2x-cosx=0
2cos²x-cosx-1=0
t=cosx, t²-t-1=0
t = (1±√5)/2
(1+√5)/2 - не подходит
t=(1-√5)/2, cosx=(1-√5)/2
x = ±arccos((1-√5)/2)+2πk
1) sinx(sinx-1)=0, sin x =0, x=
, sinx =1, x=2πk
2) cosx(√3sinx+cosx)=0, cos x =0, x=π/2+πk; 2sin(x+π/6)=0, x = -π/6+πk
Пошаговое объяснение:
3) cos3x+cos5x=0
2cos4xcosx=0
cos4x=0, 4x = π/2+πk, x=π/8 + πk/4
cosx =0 x=π/2+πk
4) sin3x+sinx=sin2x
2sinxcos2x=sin2x=2sinxcosx
sin x=0, x=πk
cos2x-cosx=0
2cos²x-cosx-1=0
t=cosx, t²-t-1=0
t = (1±√5)/2
(1+√5)/2 - не подходит
t=(1-√5)/2, cosx=(1-√5)/2
x = ±arccos((1-√5)/2)+2πk