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AP EAMCET · Maths · Limits

\(\lim _{x \rightarrow 0} \frac{\cos 2 x-\cos 3 x}{\cos 4 x-\cos 5 x}=\)

  1. A \(\frac{5}{9}\)
  2. B \(1\)
  3. C \(\frac{3}{4}\)
  4. D \(\frac{2}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{5}{9}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \lim _{x \rightarrow 0} \frac{\cos 2 x-\cos 3 x}{\cos 4 x-\cos 5 x}=\lim _{x \rightarrow 0} \frac{-2 \sin 2 x+3 \sin 3 x}{-4 \sin 4 x+5 \sin 5 x} \\ & =\lim _{x \rightarrow 0} \frac{-4 \cos 2 x+9 \cos 3 x}{(-16) \cos 4 x+25 \cos 5…