Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

(cos 30° + sin 30° ).(cos 30° − sin 30° ) is gelijk aan	A. 1
B. 2
C. 1 −
D.
E.
F. 0

(cos 30° + sin 30° ).(cos 30° − sin 30° ) is equal to	A. 1
B. 2
C. 1 −
D.
E.
F. 0

1^ste manier :
$\\(\cos30^\circ+\sin30^\circ).(\cos30^\circ-\sin30^\circ)=\left(\frac{\sqrt3}{2}+\frac12\right).\left(\frac{\sqrt3}{2}-\frac12\right)=\frac{\sqrt3+1}{2}.\frac{\sqrt3-1}{2}=\frac{(\sqrt3+1).(\sqrt3-1)}{4}=\frac{3-1}{4}=\frac12$
2^de manier :
$\\(\cos30^\circ+\sin30^\circ).(\cos30^\circ-\sin30^\circ)=\cos^230^\circ-\sin^230^\circ=\left(\frac{\sqrt3}{2}\right)^2-\left(\frac12\right)^2\\=\frac34-\frac14=\frac12$
3^de manier : (5^de jaar)
$\\(\cos30^\circ+\sin30^\circ).(\cos30^\circ-\sin30^\circ)=\cos^230^\circ-\sin^230^\circ=\cos 60^\circ=\frac12$