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Question

$\mathop {\lim }\limits_{x \to \pi /2} \tan x\log \sin x = $

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Answer

a
(a) $\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \,\tan x\log \,\sin x = \mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{\log \sin x}}{{\cot x}}$

$ = \mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{\frac{1}{{\sin x}}\cos x}}{{ - {\rm{cose}}{{\rm{c}}^{\rm{2}}}x}} = 0$ (Applying $ L-$ Hospital’s rule)

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