JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim _{x \rightarrow \frac{\pi}{2}} \frac{\left[1-\tan \left(\frac{x}{2}\right)\right][1-\sin x]}{\left[1+\tan \left(\frac{x}{2}\right)\right][\pi-2 x]^3} \text { is }

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Correct option: D

\frac{1}{32}

Option D (

\frac{1}{32}

) is correct because after applying L'Hopital's rule and trigonometric identities, the limit evaluates to

\frac{1}{32}

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