[math]\displaystyle \lim_{x \to 0} \left(\frac{1}{x^2}-\frac{1}{\tan^2 x}\right) =[/math] ? How do I prove this : [math]\displaystyle \frac{\tan x}{x}\gt\frac{x}{\sin x}[/math] when [math] x\in \left(0, \frac{\pi}{2}\right)?[/math]