mathop {lim }limits_{theta to pi /6} frac{{co | vedclass

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(B) We are given the limit: $\mathop {\lim }\limits_{	heta 	o \pi /6} \frac{{\cot^2 	heta - 3}}{{\csc 	heta - 2}}$.Using the identity $\cot^2 	he

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) We are given the limit: $\mathop {\lim }\limits_{	heta 	o \pi /6} \frac{{\cot^2 	heta - 3}}{{\csc 	heta - 2}}$.Using the identity $\cot^2 	heta = \csc^2 	heta - 1$,the expression becomes:$\mathop {\lim }\limits_{	heta 	o \pi /6} \frac{{\csc^2 	heta - 1 - 3}}{{\csc 	heta - 2}} = \mathop {\lim }\limits_{	heta 	o \pi /6} \frac{{\csc^2 	heta - 4}}{{\csc 	heta - 2}}$.Factoring the numerator as a difference of squares:$\mathop {\lim }\limits_{	heta 	o \pi /6} \frac{{(\csc 	heta - 2)(\csc 	heta + 2)}}{{\csc 	heta - 2}}$.Canceling the common term $(\csc 	heta - 2)$:$\mathop {\lim }\limits_{	heta 	o \pi /6} (\csc 	heta + 2) = \csc(\pi /6) + 2$.Since $\csc(\pi /6) = 2$,we have $2 + 2 = 4$.

$\mathop {\lim }\limits_{\theta \to \pi /6} \frac{{\cot^2 \theta - 3}}{{\csc \theta - 2}} = $

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