Question 419227
Let's rewrite the equation to make it a bit more clear:
cosxsinx - sinx = 0
(cosx)(sinx) - (sinx) = 0

This looks like an equation: ab - b = 0
If you had to factor b out of this, it would look like:
b (a - 1) = 0

So it is with the trig equation factoring out sinx

(sinx) (cosx - 1) = 0