Question:
$\lim _{x \rightarrow 0} \frac{x \cot (4 x)}{\sin ^{2} x \cot ^{2}(2 x)}$ is equal to :-
Correct Option: 1
Solution:
$\lim _{x \rightarrow 0} \frac{x \tan ^{2} 2 x}{\tan 4 x \sin ^{2} x}=\lim _{x \rightarrow 0} \frac{x\left(\frac{\tan ^{2} 2 x}{4 x^{2}}\right) 4 x^{2}}{\left(\frac{\tan 4 x}{4 x}\right) 4 x\left(\frac{\sin ^{2} x}{x^{2}}\right) x^{2}}=1$