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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\lim _{x \rightarrow 0} \frac{\tan (x)+4 \tan (2 x)-3 \tan (3 x)}{x^2 \tan (x)}\) is equal to

  1. A \(8\)
  2. B \(-8\)
  3. C \(16\)
  4. D \(-16\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(-16\)

Step-by-step Solution

Detailed explanation

\(\lim _{x \rightarrow 0} \frac{\tan x+4 \tan 2 x-3 \tan 3 x}{x^2 \tan x}\) \(=\lim _{x \rightarrow 0}\left[\frac{\tan x+4\left(\frac{2 \tan x}{1-\tan ^2 x}\right)-3\left(\frac{3 \tan x-\tan ^3 x}{1-3 \tan ^2 x}\right)}{x^2 \tan x}\right]\)…