Question

$\underset{x\to 0}{lim}\frac{1-\cos 2x}{3{\tan }^{2}x}$=

Answer 1

As we know, $1-cos2x=2si{n}^{2}x$

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