Question

2sinxcosx=0

Answer 1

sinx=0 or cosx=0
x = 0 + n*pi
x = pi/2 + n* pi

If you only want answers from 0 to 2pi, it's x = 0, pi/2, pi, 3pi/2, 2pi.....

Answer 2

Another possibility: use the formula 2sinxcosx=sin2x.

Then sin2x=0, so

\(2x=k\pi\), so

\(x=\frac{k}{2}\pi\), leading to the same numbers as @chetan552's.