# Find the exact value of each of the following.cos195^(circ)

Find the exact value of each of the following.
$\mathrm{cos}{195}^{\circ }$

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brawnyN

1:
$\mathrm{cos}{195}^{\circ }=\mathrm{cos}\left({150}^{\circ }+{45}^{\circ }\right)$
2:
$=\mathrm{cos}{150}^{\circ }\mathrm{cos}{45}^{\circ }-\mathrm{sin}{150}^{\circ }\mathrm{sin}{54}^{\circ }$
3:
$=-\frac{\sqrt{3}}{2}×\frac{\sqrt{2}}{2}-\frac{1}{2}×\frac{\sqrt{2}}{2}$
4:
$=-\frac{\sqrt{3}×\sqrt{2}}{4}-\frac{\sqrt{2}}{4}$
Result
$-\sqrt{2}\left(\sqrt{3+1}\right)$