Verified Solution • 2025–26 Session moderate

QJEEM19Macaac: JEE Main 2019 Mathematics - Class 12 JEEM19Macaac Solution: lim x → 0 ⁡ x cot ⁡ ( 4 x ) sin 2 x cot 2 ( 2 x ) is equal to :

lim_{x \to 0} \frac{x \cot (4 x)}{\sin^{2} x \cot^{2} (2 x)}

is equal to :

Multiple Choice Options

A 0
B 4
C 1
D 2

Step-by-Step Verified Solution

lim_{x \to 0} \frac{x \tan^{2} 2 x}{\tan 4 x \sin^{2} x} = lim_{x \to 0} \frac{x (\frac{\tan^{2} 2 x}{4 x^{2}}) 4 x^{2}}{(\frac{\tan 4 x}{4 x}) 4 x (\frac{\sin^{2} x}{x^{2}}) x^{2}} = 1

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