Lim x -21-sin x-cos 2 x

Lim_x →π/21 sin x/cos^2 x = lim_x →x/21 sin x /1 sin^2 x = lim_x →x/2(1 sin x)/(1 sin x ) (1 + sin x) = lim_x →x/21/1+ sin x = 1/1+ sin π/2 = 1/1+1 = 1/2 ...

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Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

lim x →π/21-s...

Question

${lim}_{x \to \frac{π}{2}} \frac{1 - s i n x}{c o s^{2} x}$

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Solution

${lim}_{x \to \frac{π}{2}} \frac{1 - sin x}{{cos}^{2} x}$
$= {lim}_{x \to \frac{x}{2}} \frac{1 - sin x}{1 - {sin}^{2} x} = {lim}_{x \to \frac{x}{2}} \frac{(1 - sin x)}{(1 - sin x) (1 + sin x)}$
$= {lim}_{x \to \frac{x}{2}} \frac{1}{1 + sin x} = \frac{1}{1 + s i n \frac{π}{2}}$
$= \frac{1}{1 + 1} = \frac{1}{2}$

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limx→π21−sinxcos2x

limx→π21−sinxcos2x =limx→x21−sinx1−sin2x=limx→x2(1−sinx)(1−sinx)(1+sinx) =limx→x211+sinx=11+sinπ2 =11+1=12

${lim}_{x \to \frac{π}{2}} \frac{1 - s i n x}{c o s^{2} x}$