I haven't tried to work it all out but I would suggest that you write .
f(z) = sin(2z). I have so far got to:
f(x + iy) = sin[2(x+iy)
f(x + iy) = sin(2x) cos(2iy) + cos(2x) sin(2iy).
I'm stuck on converting this into the form f(x + iy) = u(x,y) + iv(x,y).
Any help on that step? After that step I should be ok.