# Determine the exact value of expression. sec(210)timescot(300)+sin(225)

Determine the exact value of expression.
$\mathrm{sec}\left(210\right)×\mathrm{cot}\left(300\right)+\mathrm{sin}\left(225\right)$
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Given,
$\mathrm{sec}\left(210\right)×\mathrm{cot}\left(300\right)+\mathrm{sin}\left(225\right)$
Now,
$\mathrm{sec}\left(210\right)×\mathrm{cot}\left(300\right)+\mathrm{sin}\left(225\right)$
$=\mathrm{sec}\left(180+30\right)×\mathrm{cot}\left(360-60\right)+\mathrm{sin}\left(180+45\right)$
$=-\mathrm{sec}\left(30\right)×\left(-\mathrm{cot}\left(60\right)\right)+\left(-\mathrm{sin}\left(45\right)\right)$
$=-\left(\frac{2}{\sqrt{3}}\right)×\left(-\frac{1}{\sqrt{3}}\right)+\left(\frac{1}{\sqrt{2}}\right)$
$=\frac{2}{3}-\frac{1}{\sqrt{2}}$
$=\frac{2\sqrt{2}+3}{3\sqrt{2}}$
Jeffrey Jordon