Question

The value of $ \displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\text{cosec} 3 x}$ is equal to

• A. $\frac{4}{3}$
• B. $\frac{3}{4}$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$
• E. 0

Answer 1

Answer: (B)

Given, $\displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\operatorname{cosec} 3 x}$
$=\displaystyle\lim _{x \rightarrow 0}\left(\frac{\sin 3 x}{\tan 4 x}\right)$
$\displaystyle\lim _{x \rightarrow 0} \frac{\frac{\sin 3 x}{3 x} \times 3 x}{\frac{\tan 4 x}{4 x} \times 4 x}$
$=\displaystyle\lim _{x \rightarrow 0} \frac{3 x}{4 x}=\frac{3}{4}$