Решить тригонометрические уравнения 1) cos^2(x)+sinx-1=0 2) sin5x*cosx+sinx*cos5x=1 3) 3sin-9cosx=0 4) sin2x+sinx=0 5) 3sin^2(7/2x)-cos^2(7/2)x=-1/2

2) формула sin(a+b) sin(5x+x)=1 sin6x=1 6x=pi/2+2pik x=pi/12+pik/3 4)2sinxcosx+sinx=0 sinx(2cosx+1)=0 sinx=0 x=pik cosx=-1/2 x=pi-pi/3=2pi/3

1) cos^2(x)+sinx-1=0 1-sin²x+sinx-1=0 sinx-sin²x=0 sinx(1-sinx)=0 sinx=0⇒x=πn,n∈z sinx=1⇒x=π/2+2πk,k∈z 2) sin5x*cosx+sinx*cos5x=1 sin(5x+x)=1 sin6x=1⇒6x=π/2+2πn⇒x=π/12+πn/3,n∈z 3) 3sin-9cosx=0/cosx 3tgx-9=0 3tgx=9 tgx=3 x=arctg3+πn,n∈z 4) sin2x+sinx=0 2sinxcosx+sinx=0 sinx(2cosx+1)=0 sinx=0⇒x=πn,n∈z cosx=-1/2⇒x=+-2π/3+2πk,k∈z  5) 3sin^2(7/2x)-cos^2(7/2)x=-1/2 3/2*(1-cos7x)-1/2*(1+cos7x)=-1/2 3-3cos7x-1-cos7x=-1 4cos7x=3 cos7x=3/4 7x=+-arccos3/4+2πn x=+-1/7*arccos0,75+2πn/7,n∈z