# <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-TeXAtom-ORD">

$\underset{x\to 0}{lim}\frac{\left(\mathrm{cos}\left(\frac{\pi }{2\mathrm{cos}\left(x\right)}\right)\right)}{\mathrm{sin}\left(\mathrm{sin}{\left(x\right)}^{2}\right)}=l$
then find the value of {l}, where {l} denotes fractional part.
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Jayvion Tyler
This step is incorrect .It should have been:
$=\underset{x\to 0}{lim}\frac{\frac{\pi }{2}\left(\frac{\left(\mathrm{cos}\phantom{\rule{mediummathspace}{0ex}}\left(x\right)-1\right)}{\mathrm{cos}\left(x\right)}\right)}{{x}^{2}}=\underset{x\to 0}{lim}\frac{\frac{\pi }{2}\left(-\frac{1}{2}\right)}{1}$
as and $\underset{x\to 0}{lim}\mathrm{cos}x=1$