Question

Performance task trigonometric identities

Answer 1

#1

$\\ \sf\longmapsto cos75°$

$\\ \sf\longmapsto cos(45+30)°$

$\\ \sf\longmapsto cos45cos30+sin45.sin30$

$\\ \sf\longmapsto \dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}\times \dfrac{1}{2}$

$\\ \sf\longmapsto \dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}$

$\\ \sf\longmapsto \dfrac{\sqrt{3}+1}{2\sqrt{2}}$

#2

$\\ \sf\longmapsto tan\left(-\dfrac{\pi}{12}\right)$

$\\ \sf\longmapsto tan(-15°)$

$\\ \sf\longmapsto \dfrac{sin(-15)}{cos(-15)}$

$\\ \sf\longmapsto \dfrac{-sin15}{cos15}$

$\\ \sf\longmapsto -\dfrac{\dfrac{\sqrt{3}-1}{2\sqrt{2}}}{\dfrac{\sqrt{3}+1}{2\sqrt{2}}}$

$\\ \sf\longmapsto -\left(\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right)$