Find all solutions of the given equation in the interval 02m

Find all solutions of the given equation in the interval [0,2mu). sin5c+sin3x=0

sin5x+sin3x=0

sina+sinb=2sin((a+b)/2)cos((a-b)/2)

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

2sin(4x)cos(x)=0

sin(4x)

0<=x<=2pi ==> 0<=4x<8pi

4x =0, pi,2pi,3pi,4pi,5pi,6pi,7pi

x =0, pi/4,pi/2,3pi/4,pi,5pi/4,3pi/3,7pi/4

cos(x)=0

x=pi/2,3pi/2