$$\frac{1-\sin^{2}x.\cot^{2}x}{2\ \sin^{2}x+2\ \cos^{2}x}$$
$\frac{\left(\cos(x\left(\cot(x)\right)^{2})\right)^{2}}{2}$
$-\frac{\cot(x)\left(\sin(2x)-4x\right)\sin(2x\left(\cot(x)\right)^{2})}{4\left(\sin(x)\right)^{2}}$
