Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

(cos 15° + cos 45° + cos 75°)² is gelijk aan	A. 2 + 2
B. 2
C. 2 +
D. 4
E. 2 +

(cos 15° + cos 45° + cos 75°)² equals	A. 2 + 2
	B. 2
	C. 2 +
	D. 4
	E. 2 +

$\left(\cos15^\circ+\cos45^\circ+\cos75^\circ\right)^2=\left(\cos45^\circ+2.\cos45^\circ.\cos(-30^\circ)\right)^2\\=\left(\frac{\sqrt2}{2}+2.\frac{\sqrt2}{2}.\frac{\sqrt3}{2}\right)^2=\left(\frac{\sqrt2}{2}+\frac{\sqrt2}{2}.{\sqrt3}\right)^2=\left(\frac{\sqrt2}{2}\right)^2\!\cdot(1+\sqrt3)^2\\=\frac12.(1+2\sqrt3+3)=\frac12.(4+2.\sqrt3)=2+\sqrt3\approx 3,7$