The value of l i m x → 0 x c o t 4 x t a n 2 3 x c o t 2 6 x is equal to

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Question: Answered & Verified by Expert

The value of

\underset{x \to 0}{l i m} \frac{x c o t (4 x)}{t a n^{2} (3 x) c o t^{2} (6 x)}

is equal to

MathematicsLimitsJEE Main

Options:

A $0$
B $4$
C $\frac{2}{9}$
D $1$

Solution:

1645 Upvotes Verified Answer

The correct answer is:

1

\underset{x \to 0}{l i m} \frac{9 x^{2}}{{(\tan 3 x)}^{2}} \frac{1}{9 x} \cdot \frac{{(\tan 6 x)}^{2}}{36 \cdot x^{2}} \cdot \frac{4 x}{(\tan 4 x)} \frac{36 x^{2}}{4 x}

= 1 \times \frac{1}{9} \times 1 \times 1 \times \frac{36}{4} = 1

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