JEE Main Solved Paper 2017 Question 20

Question: $ \underset{x\to \frac{\pi }{2}}{\mathop{\lim }},\frac{\cot x-\cos x}{{{(\pi -2x)}^{3}}} $ [JEE Main Solved Paper-2017]

Options:

A) $ \frac{1}{4} $

B) $ \frac{1}{24} $

C) $ \frac{1}{16} $

D) $ \frac{1}{8} $

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Answer:

Correct Answer: C

Solution:

$ \underset{x\to \frac{\pi }{2}}{\mathop{\lim }},\frac{\cot x(1-\sin x)}{-8{{( x-\frac{\pi }{2} )}^{3}}} $

$ =\underset{x\to \frac{\pi }{2}}{\mathop{\lim }},\frac{\tan ( \frac{\pi }{2}-x )}{8( \frac{\pi }{2}-x )}\frac{( 1-\cos ( \frac{\pi }{2}-x ) )}{{{( \frac{\pi }{2}-x )}^{2}}} $ $ =\frac{1}{8}.1.\frac{1}{2}=\frac{1}{16} $