Notes: `195^@ = 225^@ - 30^@` Find the exact values of the sine, cosine, and tangent of the angle.

$\displaystyle{\sin{{\left({u}-{v}\right)}}}={\sin{{\left({u}\right)}}}{\cos{{\left({v}\right)}}}-{\cos{{\left({u}\right)}}}{\sin{{\left({v}\right)}}}$

$\displaystyle{\sin{{\left({225}-{30}\right)}}}={\sin{{\left({225}\right)}}}{\cos{{\left({30}\right)}}}-{\cos{{\left({225}\right)}}}{\sin{{\left({30}\right)}}}$

$\displaystyle{\sin{{\left({225}-{30}\right)}}}={\left(-\frac{\sqrt{{2}}}{{2}}\right)}{\left(\frac{\sqrt{{3}}}{{2}}\right)}-{\left(-\frac{\sqrt{{2}}}{{2}}\right)}{\left(\frac{{1}}{{2}}\right)}=-\frac{\sqrt{{2}}}{{4}}{\left(\sqrt{{3}}-{1}\right)}$

$\displaystyle{\cos{{\left({u}-{v}\right)}}}={\cos{{\left({u}\right)}}}{\cos{{\left({v}\right)}}}+{\sin{{\left({u}\right)}}}{\sin{{\left({v}\right)}}}$

$\displaystyle{\cos{{\left({225}-{30}\right)}}}={\cos{{\left({225}\right)}}}{\cos{{\left({30}\right)}}}+{\sin{{\left({225}\right)}}}{\sin{{\left({30}\right)}}}$

$\displaystyle{\cos{{\left({225}-{30}\right)}}}={\left(-\frac{\sqrt{{2}}}{{2}}\right)}{\left(\frac{\sqrt{{3}}}{{2}}\right)}+{\left(-\frac{\sqrt{{2}}}{{2}}\right)}{\left(\frac{{1}}{{2}}\right)}=-\frac{\sqrt{{2}}}{{4}}{\left(\sqrt{{3}}+{1}\right)}$

$\displaystyle{\tan{{\left({u}-{v}\right)}}}=\frac{{{\tan{{\left({u}\right)}}}-{\tan{{\left({v}\right)}}}}}{{{1}+{\tan{{\left({u}\right)}}}{\tan{{\left({v}\right)}}}}}$

$\displaystyle{\tan{{\left({225}-{30}\right)}}}=\frac{{{\tan{{\left({225}\right)}}}-{\tan{{\left({30}\right)}}}}}{{{1}+{\tan{{\left({225}\right)}}}{\tan{{\left({30}\right)}}}}}=\frac{{{1}-{\left(\frac{\sqrt{{3}}}{{3}}\right)}}}{{{1}+{\left({1}\right)}{\left(\frac{\sqrt{{3}}}{{3}}\right)}}}=\frac{{{3}-\sqrt{{3}}}}{{{3}+\sqrt{{3}}}}$