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  4. displaystyle limx→0 (x cot(4x)/ sin2 x cot2 (2x)) is equal to :

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Q. $\displaystyle\lim_{x\to0} \frac{x\cot\left(4x\right)}{\sin^{2} x \cot^{2} \left(2x\right)} $ is equal to :

JEE MainJEE Main 2019Limits and Derivatives

Solution:

$\lim_{x\to0} \frac{x\tan^{2} 2x}{\tan 4x \sin^{2} x} =\lim_{x\to0} \frac{x\left(\frac{\tan^{2}2x}{4x^{2}}\right)4x^{2}}{\left(\frac{\tan4x}{4x}\right)4x\left(\frac{\sin^{2}x}{x^{2}}\right)x^{2}} = 1 $