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TS EAMCET · Maths · Limits

\(\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{\sin ^4 x}=\)

  1. A \(\frac{1}{2}\)
  2. B \(\frac{1}{4}\)
  3. C \(\frac{1}{6}\)
  4. D \(\frac{1}{8}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{8}\)

Step-by-step Solution

Detailed explanation

Given that, \(\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{\sin ^4 x}\) \(=\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{(1-\cos x)^2} \times \frac{(1-\cos x)^2}{x^4} \times \frac{x^4}{\sin ^4 x}\)…