The correct option is B 2/π lim _ x→π #160; 2 #160; x #160;x x =lim _ x→π #160; 2 #160; 1 cos #160;x xsin x #160; =2π ...

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Substitution Method to Remove Indeterminate Form

limx →π/2cose...

Question

$lim x \to \frac{π}{2} \frac{c o s e c x - cot x}{x}$ =

1

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\frac{2}{π}

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\frac{1}{2}

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\frac{1}{5}

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Solution

The correct option is B $\frac{2}{π}$
$lim x \to \frac{π}{2} \frac{csc x - cot x}{x}$
$= lim x \to \frac{π}{2} \frac{1 - cos x}{x sin x}$
$= \frac{2}{π}$

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