Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

tan 105° =	A. − 1
B. − 2
C. 2 +
D. − 2 +
E. − 2 −

$https://latex.codecogs.com/png.image?\dpi{110}\tan 105^\circ = \tan(45^\circ+60^\circ)=\frac{\tan 45^\circ+\tan 60^\circ}{1-\tan 45^\circ.\tan 60^\circ}=\frac{1+\tan 60^\circ}{1-\tan 60^\circ}\\=\frac{1+\sqrt3}{1-\sqrt3}=\frac{(1+\sqrt3)^2}{(1-\sqrt3)(1+\sqrt3)}=\frac{1+2\sqrt3+3}{1-3}=\frac{4+2\sqrt3}{-2}=-2-\sqrt3$