Answer
$sin~375°=\frac{\sqrt 6-\sqrt 2}{4}$
$cos~375°=\frac{\sqrt 6+\sqrt 2}{4}$
$tan~375°=\frac{\sqrt 3-1}{\sqrt 3+1}$
Work Step by Step
$sin~375°=sin~(135°+240°)=sin~135°~cos~240°+cos~135°~sin~240°=\frac{\sqrt 2}{2}(-\frac{1}{2})+(-\frac{\sqrt 2}{2})(-\frac{\sqrt 3}{2})=-\frac{\sqrt 2}{4}+\frac{\sqrt 6}{4}=\frac{\sqrt 6-\sqrt 2}{4}$
$cos~375°=cos~(135°+240°)=cos~135°~cos~240°-sin~135°~sin~240°=-\frac{\sqrt 2}{2}(-\frac{1}{2})-\frac{\sqrt 2}{2}(-\frac{\sqrt 3}{2})=+\frac{\sqrt 2}{4}+\frac{\sqrt 6}{4}=\frac{\sqrt 6+\sqrt 2}{4}$
$tan~375°=tan(135°+240°)=\frac{tan~135°+tan~240°}{1-tan~135°~tan~240°}=\frac{-1+\sqrt 3}{1-(-1)\sqrt 3}=\frac{\sqrt 3-1}{\sqrt 3+1}$
