solve the eqns for 0<=x<=180

1. sin3x+sinx=0

(i don't get my friend's working):

2 sin2xcosx=0

2(2sinxcosx)(cosx)=0

(4sinxcosx)(cosx)=0

4 sinx=0

sinx=0

x= 0, 180

what I don't get is how the(4 sin x cos x) (cos x) = 0became just4 sin x = 0.

she said she canceled it and gave no further explanation. i don't get it, because it's multiply, how could she have canceled thecos x-es out.

2. sin5x-sinx=0

i got up until:

2 cos 3x sin 2x = 0

2 (4cos*3x-3cosx) (2 sinx cosx) = 0