Verified answer

sin(3x)=cos(5x)

cos(5x)-sin(3x)=0

cos5x-cos(pi/2-3x)=0

-2sin((5x+pi/2-3x)/2)sin((5x-pi/2+3x)/2=0

2sin(x+pi/4)*sin(4x-pi/4)=0

a) sin(x+pi/4)=0

x+pi/4=pi*n

x=pi*n-pi/4

б) sin(4x-pi/4)=0

4x-pi/4=0

4x-pi/4=pi*n

4x=pi/4  +pi*n

x=pi/16  +pi*n/4