[TEX]3sin^2(\frac{x}{2})cos(\frac{3pi}{2}+\frac{x}{2})+3sin^2(\frac{x}{2})cos(\frac{x}{2})=sin(\frac{x}{2})cos^2(\frac{x}{2})+sin^2(\frac{x}{2}+\frac{pi}{2})cos(\frac{x}{2})[/TEX]
[TEX]3sin^2(\frac{x}{2})sin(\frac{x}{2})+3sin^2(\frac{x}{2})cos(\frac{x}{2})=sin(\frac{x}{2})cos^2(\frac{x}{2})+cos^2(\frac{x}{2})cos(\frac{x}{2})[/TEX]
[TEX]3sin^2(\frac{x}{2})[sin(\frac{x}{2})+cos(\frac{x}{2})]=cos^2(\frac{x}{2})[sin(\frac{x}{2})+cos(\frac{x}{2})][/TEX]
[TEX][sin(\frac{x}{2})+cos(\frac{x}{2})].[3sin^2(\frac{x}{2})-cos^2(\frac{x}{2})]=0[/TEX]
[TEX][sin(\frac{x}{2})+cos(\frac{x}{2})].[4sin^2(\frac{x}{2})-1]=0[/TEX]