TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right)=\)
- A \(\frac{\pi}{2}\)
- B \(\frac{2}{\pi}\)
- C \(1\)
- D \(0\)
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…
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