Lim x -4cosec2 x-2- x-1

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

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x →π/4cos...

Question

${lim}_{x \to \frac{π}{4}} \frac{c o s e c^{2} x - 2}{c o t x - 1}$

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Solution

${lim}_{x \to \frac{π}{4}} \frac{c o s e c^{2} x - 2}{c o t x - 1}$

$= {lim}_{x \to \frac{π}{4}} \frac{c o t^{2} x + 1 - 2}{c o t x - 1}$

$= {lim}_{x \to \frac{π}{4}} \frac{c o t^{2} x - 1}{c o t x - 1}$

$= {lim}_{x \to \frac{π}{4}} \frac{(c o t x - 1) (c o t x + 1)}{(c o t x - 1)}$

$= {lim}_{x \to \frac{π}{4}} (c o t x + 1)$

$= c o t \frac{π}{4} + 1$

=1+1=2

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limx→π4cosec2x−2cotx−1

limx→π4cosec2x−2cotx−1 =limx→π4cot2x+1−2cotx−1 =limx→π4cot2x−1cotx−1 =limx→π4(cotx−1)(cotx+1)(cotx−1) =limx→π4(cotx+1) =cotπ4+1 =1+1=2

${lim}_{x \to \frac{π}{4}} \frac{c o s e c^{2} x - 2}{c o t x - 1}$