#1
[tex]\\ \sf\longmapsto cos75°[/tex]
[tex]\\ \sf\longmapsto cos(45+30)°[/tex]
[tex]\\ \sf\longmapsto cos45cos30+sin45.sin30[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}\times \dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{\sqrt{3}+1}{2\sqrt{2}}[/tex]
#2
[tex]\\ \sf\longmapsto tan\left(-\dfrac{\pi}{12}\right)[/tex]
[tex]\\ \sf\longmapsto tan(-15°)[/tex]
[tex]\\ \sf\longmapsto \dfrac{sin(-15)}{cos(-15)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-sin15}{cos15}[/tex]
[tex]\\ \sf\longmapsto -\dfrac{\dfrac{\sqrt{3}-1}{2\sqrt{2}}}{\dfrac{\sqrt{3}+1}{2\sqrt{2}}}[/tex]
[tex]\\ \sf\longmapsto -\left(\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right)[/tex]
