The correct option is A 1 lim _ x→π nbsp; 2 nbsp; (π nbsp; 2 x) nbsp;x x nbsp; =lim _ h→ 0 (π nbsp; 2 π nbsp; 2 +h) (π nbsp; ...

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Substitution Method to Remove Indeterminate Form

limx→π2π2-x x...

Question

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

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-1

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\frac{1}{π}

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Solution

The correct option is A 1
$lim x \to \frac{π}{2} \frac{(\frac{π}{2} - x) sec x}{csc x}$
$= lim h \to 0 \frac{(\frac{π}{2} - \frac{π}{2} + h) sec (\frac{π}{2} - h)}{csc (\frac{π}{2} - h)}$
$= lim h \to 0 \frac{h csc h}{sec h}$
$= lim h \to 0 \frac{h cos h}{sin h} = 1$

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