It's been a while since I did similtaneous equations but here goes.

c) (tanx sinx)/tanx - sinx = (tanx + sinx)/(tanx sinx)

tanx sinx = (tanx + sinx)/(tanx sinx) + sinx * tanx
tanx = (tanx + sinx)/(tanx sinx) + sinx - (tanx sinx)
sinx = (tanx + sinx)/(tanx sinx) * tanx - (tanx sinx)