How to solve trigonometric equations by factoring?

Solving trigonometric equations by factoring isn't hard at all, it is very very similar to solving algebraic equations by factoring. This is how we start if we were giving this problem:

sinxcosx-3cosx=0 

We first factor out cosine, and we get cosx(sinx-3). Then, we set both cosx to 0 and sinx-3 to zero and than we solve. We should get sinx equals 3 and cosx equals 0. We than use arcsin and we get that cosx is equal to 90. We find all the other solutions by finding its reference angle, so that means cosx is equal to 90 and 270. Now, sinx=3 isnt possible. The unit circle only goes up to 1 because the radius is 1, therefore the only solutions are 90 and 270. 

And, viola! Thats how you solve trigonometric equations by factoring.

Try this:

sinxcosx=-cosx