1. cos3x=2sin(3π/2-x) 2. cosx-sin11x=o 3. sinx+sin7x-cos5s-cos(π-3x)=o

1
cos3x=-2cosx
4cos³x-3cosx+2cosx=0
4cos³x-cosx=0
cosx(4cos²x-1)=0
cosx=0⇒x=π/2+πn,n∈z
4cos²x-1=0
4(1+cos2x)/2=1
1+cos2x=1/2
cos2x=-1/2
2x=+-2π/3+2πk
x=+-π/3+πk,k∈z
2
cosx-cos(π/2-11x)=0
-2sin(6x-π/4)sin(-5x+π/4)=0
2sin(6x-π/4)sin(5x-π/4)=0
sin(6x-π/4)=0
6x-π/4=πn
6x=π/4+πn
x=π/24+πn/6,n∈z
sin(5x-π/4)=0
5x-π/4=πk
5x=π/4+πk
x=π/20+πk/5,k∈z
3
(sinx+sin7x)+(cos3x-cos5x)=0
2sin4xcos3x+2sin4xsinx=0
2sin4x*(cos3x+sinx)=0
sin4x=0
4x=πn
x=πn/4
cos3x+cos(π/2-x)=0
2cos(x+π/4)cos(2x-π/4)=0
cos(x+π/4)=0
x+π/4=π/2+πk
x=π/4+πk,k∈z
cos(2x-π/4)=0
2x-π/4=π/2+πm
2x=3π/4+πm
x=3π/8+πm/2,m∈z