cos195-cos45/sin195-sin45

[tex] \frac{cos 195 - cos 45}{sin 195 - sin 45} [/tex]

= [tex] \frac{cos (180+15) - \frac{\sqrt{2}}{2}}{sin (180+15) - \frac{\sqrt{2}}{2}} [/tex]

= [tex] \frac{cos (180-15) - \frac{\sqrt{2}}{2}}{-sin (180-15) - \frac{\sqrt{2}}{2}} [/tex]

= [tex] \frac{-cos 15 - \frac{\sqrt{2}}{2}}{-sin 15- \frac{\sqrt{2}}{2}} [/tex]

= [tex] \frac{-(\frac{\sqrt{6}+\sqrt{2}}{4}) - \frac{\sqrt{2}}{2}}{-(\frac{\sqrt{6}-\sqrt{2}}{4}) - \frac{\sqrt{2}}{2}} [/tex]

= [tex] \frac{-(\sqrt{6}+\sqrt{2}+2\sqrt{2})}{-(\sqrt{6}-\sqrt{2}) -2\sqrt{2}} [/tex]

= [tex] \frac{(\sqrt{6}+2\sqrt{2})+\sqrt{2}}{(\sqrt{6}+2\sqrt{2})-\sqrt{2}} . \frac{(\sqrt{6}+2\sqrt{2})+\sqrt{2}}{(\sqrt{6}+2\sqrt{2})+\sqrt{2}} [/tex]