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AP EAMCET · Maths · Limits

\(\lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 3 x)(\operatorname{cosec} x-\cot x)^2}=\)

  1. A \(\frac{4}{9}\)
  2. B \(\frac{8}{9}\)
  3. C \(\frac{16}{9}\)
  4. D \(\frac{32}{9}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{16}{9}\)

Step-by-step Solution

Detailed explanation

\( \lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 3 x)(\operatorname{cosec} x-\cot x)^2} \) \( = \lim _{x \rightarrow 0} \frac{x(\tan 2 x-2 \tan x)}{(1-\cos 3 x)\left(\frac{1-\cos x}{\sin x}\right)^2} \)…