lim x → 0 s i n 2 x c o t 2 ( 2 x ) x c o t ( 4 x ) is equal to:

lim x → 0 s i n 2 x ⋅ c o t 2 2 x x c o t 4 x = lim x → 0 s i n 2 x ⋅ t a n 4 x x ⋅ t a n 2 2 x = lim x → 0 ( s i n x x ) 2 ⋅ ( 2 x t a n 2 x ) 2 ⋅ ( t a n 4 x 4 x ) ⋅ 2 2 4 = 1

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Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsTrigonometric and Inverse Trigonometric limitsEasy2 minPYQ_2019

MathematicsEasysingle choice

$lim_{x \to 0} \frac{x c o t ( 4 x )}{s i n ^{2} x c o t ^{2} ( 2 x )}$ is equal to:

Options:

Answer:

Solution:

$lim_{x \to 0} \frac{x c o t 4 x}{s i n ^{2} x \cdot c o t ^{2} 2 x} = lim_{x \to 0} \frac{x \cdot t a n ^{2} 2 x}{s i n ^{2} x \cdot t a n 4 x}$ $= lim_{x \to 0} (\frac{x}{s i n x})^{2} \cdot (\frac{t a n 2 x}{2 x})^{2} \cdot (\frac{4 x}{t a n 4 x}) \cdot \frac{4}{2 ^{2}} = 1$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Trigonometric and Inverse Trigonometric limits

⏱ 2mℹ️ Source: PYQ_2019

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