Question

Solve

$\underset{x\to \pi /2}{lim}(2x\tan x-\pi \sec x)$

Answer 1

${lim}_{x\to \frac{\pi }{2}}(\frac{2x\sin x}{\cos x}-\frac{\pi }{\cos x}){lim}_{x\to \frac{\pi }{2}}\left(\frac{2x\sin x-\pi }{\cos x}\right)$

Using LHR.

$\Rightarrow \left(\frac{2\sin x+2x\cos x}{-\sin x}\right)\Rightarrow \frac{2}{-1}\Rightarrow -2$