limx→π2 cot⁡x−cos⁡xπ2−x3= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Solution:

$= \underset{x \to \frac{π}{2}}{L i m} \frac{c o t x - \cos x}{{(\frac{π}{2} - x)}^{3}} l e t \frac{π}{2} - x = θ \Rightarrow \frac{π}{2} - θ = x = lim_{θ \to 0} \frac{\tan θ - \sin θ}{θ^{3}} = lim_{θ \to 0} \frac{\tan θ (1 - \cos θ)}{θ^{3}} = lim_{θ \to 0} \frac{\tan θ}{θ} \frac{(1 - \cos θ)}{θ^{2}} = lim_{θ \to 0} \frac{\tan θ}{θ} \frac{(2 \sin^{2} \frac{θ}{2})}{4 {(\frac{θ}{2})}^{2}} = \frac{1}{2} \Rightarrow 0.5$

$put θ = \frac{π}{2} - x$

$lim_{x \to \frac{π}{2}} \frac{\cot x - \cos x}{{(\frac{π}{2} - x)}^{3}} =$

Solution:

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