$4.cos(\frac{3x}{2}).cosx.sin\frac{x}{2}=4.\frac{1}{2}(sin2x-sinx).cosx=2sin2x.cosx-sin2x=sinx+sin3x-sin2x$
$4.cos(\frac{3x}{2}).cosx.sin\frac{x}{2}=4.\frac{1}{2}(sin2x-sinx).cosx=2sin2x.cosx-2sin2x=sinx+sin3x-sin2x$
$4.cos(\frac{3x}{2}).cosx.sin\frac{x}{2}=4.\frac{1}{2}(sin2x-sinx).cosx=2sin2x.cosx-sin2x=sinx+sin3x-sin2x$