Lim x -6cos 2 x-3-cosec x-2

Lim_x →π/6cot^2 x 3/cosec x 2 =lim_x →π/6(cosec^2x 1) 3/cosec x 2= lim_x →π/6(cosec^2x 4) 3/cosec x 2 =lim_x →π/6(cosec x 2)(cosec x + 2)/(cosec x 2)=lim_x ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x →π/6cos...

Question

${lim}_{x \to \frac{π}{6}} \frac{c o t^{2} x - 3}{c o s e c x - 2}$

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Solution

${lim}_{x \to \frac{π}{6}} \frac{c o t^{2} x - 3}{c o s e c x - 2}$

$= {lim}_{x \to \frac{π}{6}} \frac{(c o s e c^{2} x - 1) - 3}{c o s e c x - 2} = {lim}_{x \to \frac{π}{6}} \frac{(c o s e c^{2} x - 4) - 3}{c o s e c x - 2}$

$= {lim}_{x \to \frac{π}{6}} \frac{(c o s e c x - 2) (c o s e c x + 2)}{(c o s e c x - 2)} = {lim}_{x \to \frac{π}{6}} (c o s e c x + 2)$

$= c o s e c \frac{π}{6} + 2 = 2 + 2 = 4$

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Similar questions

${lim}_{x \to \frac{π}{6}} \frac{c o t^{2} x - 3}{c o s e c x - 2}$

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limx→π6cot2 x−3cosec x−2

limx→π6cot2 x−3cosec x−2 =limx→π6(cosec2x−1)−3cosec x−2=limx→π6(cosec2x−4)−3cosec x−2 =limx→π6(cosec x−2)(cosec x+2)(cosec x−2)=limx→π6(cosec x+2) =cosecπ6+2=2+2=4

${lim}_{x \to \frac{π}{6}} \frac{c o t^{2} x - 3}{c o s e c x - 2}$