Question

Evaluate:${lim}_{n\to \frac{\pi }{2}}\left(\frac{2x-\pi }{\cos x}\right)=$

• A. $0$
• B. $\frac{1}{2}$
• C. $-2$
• D. $5$

Answer 1

The correct option is C $-2$

let $y=\frac{\pi }{2}-x$

$\Rightarrow L=\underset{y\to 0}{lim}\frac{2(\frac{\pi }{2}-y)-\pi }{\cos (\frac{\pi }{2}-y)}$

$\Rightarrow L=\underset{y\to 0}{lim}\frac{\pi -2y-\pi }{\sin y}$

$\Rightarrow L=\underset{y\to 0}{lim}-2\left(\frac{y}{\sin y}\right)$

$\Rightarrow L=-2$

$\Rightarrow \left(C\right)$