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

Question

Aicharya · Accepted Answer

$\begin{aligned} & \operatorname{Lim}_{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right) \ & =\operatorname{Lim}_{x \rightarrow 1} \frac{1-x}{\cot \left(\frac{\pi x}{2}\right)}=\operatorname{Lim}_{x \rightarrow 1} \frac{-1}{-\frac{\pi}{2} \operatorname{cosec}^2\left(\frac{\pi x}{2}\right)} \quad \text{(on applying L'Hospital rule)} \end{aligned}$ $=\frac{2}{\pi}$ Hence, option (d) is correct.

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

Solution