1-cosx=2sin^2(x/2)
[m]\lim_{x \to 0 }\frac{2sin^2\frac{x}{2}(1+cosx+cos^2x)}{x\cdot 2sinx\cdot cosx}=\lim_{x \to 0 }\frac{2sin^2\frac{x}{2}}{x\cdot 2sinx}\cdot \lim_{x \to 0 }\frac{1+cosx+cos^2x}{cosx}=[/m]
[m]=\lim_{x \to 0 }\frac{sin\frac{x}{2}\cdot sin\frac{x}{2}}{x\cdot 2sin\frac{x}{2}\cdot cos\frac{x}{2}}\cdot \frac{1+1+1}{1}=[/m]
[m]=\lim_{x \to 0 }\frac{ sin\frac{x}{2}}{x\cdot 2\cdot cos\frac{x}{2}}\cdot 3=\frac{3}{4}[/m]