how to write the X-coordinates of the point of intersection of the graph sin2x and 1/2tanx

Answer 1

sin(2x) = 1/2 tan(x)
2sinx cosx = 1/2 sinx/cosx
4sinx cosx = sinx/cosx
Clearly, sinx=0 is one intersection

Elsewhere, we can divide through by sinx, and we have
4cos^2x = 1
cosx = ±1/2

Now you can easily find the points you want.