A) 0
B) 1
C) ?1
D) None of these
Correct Answer: A
Solution :
\[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\,\tan x\log \,\sin x=\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\log \sin x}{\cot x}\] \[=\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\frac{1}{\sin x}\cos x}{-\text{cose}{{\text{c}}^{\text{2}}}x}=0\] (Applying L-Hospital?s rule)
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