Question

$\underset{x\to \frac{\pi }{2}}{lim}[x\tan x-\frac{\pi }{2}\sec x]$ is equal to

• A. $1$
• B. $-1$
• C. $0$
• D. None of these

Answer 1

Answer: (B)

$-1$

$\underset{x\to \frac{\pi }{2}}{lim}[x\tan x-\left(\frac{\pi }{2}\right)\sec x]=\underset{x\to \frac{\pi }{2}}{lim}\frac{2x\sin x-\pi }{2\cos x}\left(\frac{0}{0}\text{form}\right)$

$=\underset{x\to \frac{\pi }{2}}{lim}\frac{[2\sin x+2x\cos x]}{-2\sin x},\text{( Applying L-Hospital's rule)}$

$=-1$