$\text{ The value of }\underset{x\to 0}{\lim }\frac{1-{\cos }^{3}x}{x\sin x\cos x}\text{ is }$

$\begin{array}{l}\underset{x\to 0}{\lim }\frac{1-{\cos }^{3}x}{x\sin x\cos x}\\ =\underset{x\to 0}{\lim }\frac{(1-\cos x)\left(1+\cos x+{\cos }^{2}x\right)}{x\sin x\cos x}\\ =\underset{x\to 0}{\lim }\frac{2{\sin }^2\left(\frac{x}{2}\right)}{x\cdot 2\sin \left(\frac{x}{2}\right)\cos \left(\frac{x}{2}\right)}\times \frac{\left(1+\cos x+{\cos }^{2}x\right)}{\cos x}\\ =\underset{x\to 0}{\lim }\frac{\sin \left(\frac{x}{2}\right)}{2\left(\frac{x}{2}\right)}\times \frac{1+\cos x+{\cos }^{2}x}{\cos \left(\frac{x}{2}\right)\cos x}=\frac{1}{2}\times 3=\frac{3}{2}.\end{array}$