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TS EAMCET · Maths · Limits

\(\lim _{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right)=\)

  1. A \(\frac{\pi}{2}\)
  2. B \(\frac{2}{\pi}\)
  3. C \(1\)
  4. D \(0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2}{\pi}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \lim _{x \rightarrow 1}(1-x) \frac{\sin \frac{\pi x}{2}}{\cos \frac{\pi x}{2}}=\lim _{1-x \rightarrow 0}(1-x) \frac{\sin \frac{\pi x}{2}}{\cos \frac{\pi x}{2}} \\ = & \lim _{1-x \rightarrow 0}(1-x) \frac{\sin \frac{\pi x}{2}}{\sin \left(\frac{\pi}{2}-\frac{\pi…