AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow \frac{\pi}{2}} \frac{1-\tan \frac{x}{2}}{1+\tan \frac{x}{2}} \cdot \frac{1-\sin x}{(\pi-2 x)^3}=\)
- A \(\frac{1}{32}\)
- B \(0\)
- C \(\frac{1}{16}\)
- D \(\frac{1}{8}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{32}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow \frac{\pi}{2}} \frac{1-\tan \frac{x}{2}}{1+\tan \frac{x}{2}} \cdot \frac{1-\sin x}{(\pi-2 x)^3} \\ & =\lim _{x \rightarrow \frac{\pi}{2}} \tan \left(\frac{\pi}{4}-\frac{x}{2}\right): \frac{1-\sin x}{(\pi-2 x)^3} \\ & \text { On putting }…
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