Solve the equation: Sin2x - Sinx = 0

We know that sin2x=2sinxcosx

(search the net for proof if you wish)

So the original equation becomes

2sinxcosx-sinx=0

The two terms both have sinx that can be taken out to get:

sinx (2cosx-1) = 0

This is true if sinx=0 or 2cosx-1=0, rewritten: cosx=1/2

sinx=0 than x=2kπ

cosx=1/2 than x=π/3+2kπ

where k is an integer