[tex]sin3x+sinx+2sin2x=2sin\left(\dfrac{3x+x}{2}\right)\cdot cos\left(\dfrac{3x-x}{2}\right)+2sin2x=\\\\=2sin2x\cdot cosx + 2sin2x=2sin2x(cosx+1)=2sin2x\cdot 2cos^2\left(\dfrac{x}{2}\right)=\\\\=4sin2x\cdot cos^2\left(\dfrac{x}{2}\right).[/tex]
Green eyes.
