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Question: \(\lim _ { x \rightarrow \pi / 2 }\) \(\frac{\sin x - (\sin x)^{\sin x}}{1 - \sin x + \mathcal{l}n\s...

lim⁡x→π/2\lim _ { x \rightarrow \pi / 2 } sin⁡x−(sin⁡x)sin⁡x1−sin⁡x+lnsin⁡x\frac{\sin x - (\sin x)^{\sin x}}{1 - \sin x + \mathcal{l}n\sin x}is equal to-

A

4

B

2

C

1

D

None of these

Answer

2

Explanation

Solution

take sin x = t

By L' Hospital =

−{tt(1/t)+tt(1+lnt)2}−1/t2\frac { - \left\{ \mathrm { t } ^ { \mathrm { t } } ( 1 / \mathrm { t } ) + \mathrm { t } ^ { \mathrm { t } } ( 1 + \mathrm { lnt } ) ^ { 2 } \right\} } { - 1 / \mathrm { t } ^ { 2 } } = 2