1
1/2*sin2x+1/2*sin12x-sin2x=0
1/2*sin12x-1/2*sin2x=0
1/2*(sin12x-sin2x)=0
1/2*sin5xcos7x=0
sin5x=0⇒5x=πn,n∈z⇒x=πn/5,n∈z
cos7x=0⇒7x=π/2+πk,k∈z⇒x=π/14+πk/7,k∈z
2
3cos2x-1=cos2x/sin2x*2sin2x*cos2x
3cos2x-1=2cos²2x
cos2x=a
2a²-3a+1=0
D=9-8=1
a1=(3-1)/4=1/2⇒cos2x=1/2⇒2x=+-π/3+2πn⇒x=+-π/6+πn,n∈z
a2=(3+1)/4=1⇒cos2x=1⇒2x=2πk⇒x=πk,k∈z
3
2sin2x*cos2x=-2sin2x*sin3x
2sin2x*(cos2x+sin3x)=0
sin2x=0⇒2x=πn⇒x=πn/2,n∈z
cos2x+sin3x=0
cos2x+cos(π/2-3x)=0
2cos(π/4-x/2)cos(5x/2-π/4)=0
2sin(x/2-π/4)cos(5x/2-π/4)=0
sin(x/2-π/4)=0⇒x/2-π/4=πn⇒x/2=π/4+πn⇒x=π/2+2πn,n∈z
cos(5x/2-π/4)=0⇒5x/2-π/4=π/2+πk⇒5x/2=3π/4+πk⇒x=3π/10+2πk/5,k∈z
4
1/2*sin(-x)+1/2*sin7x+1/2*sin(-7x)+1/2*sin9x=0
1/2*sin9x-1/2*sinx=0
1/2*(sin9x-sinx)=0
1/2*2sin4xcos5x=0
sin4x=0⇒4x=πn⇒x=πn/4,n∈z
cos5x=0⇒5x=π/2+πk⇒x=π/10+πk/5,k∈z