Limit x_0 (1-cos 2x) /x2

[tex]lim_{x \: \rightarrow 0} \frac{1 - \cos(2x) }{ {x}^{2} } \\ = lim_{x \: \rightarrow 0} \frac{1 - (1 - 2 \sin^{2} {x})}{ {x}^{2} } \\ = 2 \times lim_{x \: \rightarrow 0} \frac{ \sin^{2} {x}}{ {x}^{2} } = 2[/tex]