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

You're not sure how to factor out sin(x)? OK, let's look at this
bit of algebra:

                               AB - B = 0
                              AB - 1B = 0
                             B(A - 1) = 0

Do you understand that? I put a green 1 beside the red B. Then I factored
out the red B putting the green A and the green 1 inside the parentheses.

OK, I will use the exact same color scheme, and do the exact same thing:

                cos(x)sin(x) - sin(x) = 0
               cos(x)sin(x) - 1sin(x) = 0
                   sin(x)(cos(x) - 1) = 0

Do you understand that? I put a green 1 beside the red sin(x). Then I factored
out the red sin(x) putting the green cos(x) and the green 1 inside the parentheses.
 
Can you go from there? If not post again.  If and when you post again,
be sure to tell us whether the answer should be given in degrees or 
radians (in terms of p), and whether you want
all possible solutions or just the solutions between 0 and 2p or 0 and 360°. 

Edwin