Question

${lim}_{x\to 0}\frac{1-cos2x}{3ta{n}^{2}x}$

Answer 1

${lim}_{x\to 0}\frac{1-cos2x}{3ta{n}^{2}x}$

$={lim}_{x\to 0}\frac{2si{n}^{2}x}{3ta{n}^{2}x}$

$=\frac{2}{3}{lim}_{x\to 0}\frac{si{n}^{2}x}{\left(\frac{si{n}^{2}x}{co{s}^{2}x}\right)}$

$=\frac{2}{3}{lim}_{x\to 0}co{s}^{2}x=\frac{2}{3}$