TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{\sin ^4 x}=\)
- A \(\frac{1}{2}\)
- B \(\frac{1}{4}\)
- C \(\frac{1}{6}\)
- D \(\frac{1}{8}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{8}\)
Step-by-step Solution
Detailed explanation
Given that, \(\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{\sin ^4 x}\) \(=\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{(1-\cos x)^2} \times \frac{(1-\cos x)^2}{x^4} \times \frac{x^4}{\sin ^4 x}\)…
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