_ x 2 x x= - Vidyadip

MCQ

$\lim _{x \rightarrow \frac{\pi}{2}} \tan x \log \sin x=$

✓
$0$
B
1
C
-1
D
None of these

✓

Answer

Correct option: A.

$0$

(A)
$\lim _{x \rightarrow \frac{\pi}{2}} \tan x \log \sin x=\lim _{x \rightarrow \frac{\pi}{2}} \frac{\log \sin x}{\cot x}$
$=\lim _{x \rightarrow \frac{\pi}{2}} \frac{\frac{1}{\sin x} \cos x}{-\operatorname{cosec}^2 x}=0$
...[Applying L-Hospital's rule]

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