A) 1
B) ?1
C) 0
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to \pi /2}{\mathop{\lim }}\,\,\left[ x\tan x-\left( \frac{\pi }{2} \right)\,\sec x \right]\] \[=\underset{x\to \pi /2}{\mathop{\lim }}\,\,\,\frac{2x\,\,\sin x-\pi }{2\,\cos x}\], \[\left[ \text{form}\frac{0}{0} \right]\] \[=\underset{x\to \pi /2}{\mathop{\lim }}\,\,\,\frac{[2\,\sin x+2x\cos x]}{-2\,\sin x}=-1\],(By L-Hospital?s rule).
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