Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

cos 15° is gelijk aan	A. $\sqrt{\frac{2+\sqrt{3}}{2}}$
	B. $\sqrt{\frac{2+\sqrt{3}}{4}}$
	C. $\sqrt{\frac{2-\sqrt{3}}{2}}$
	D. $\sqrt{\frac{2-\sqrt{3}}{4}}$
	E. $\frac{\sqrt{3}}{4}$

[ 5-8102 - op net sinds 22.10.2020-(E)-21.10.2025 ]

Translation in E N G L I S H

cos 15° is equal to	A. $\sqrt{\frac{2+\sqrt{3}}{2}}$
	B. $\sqrt{\frac{2+\sqrt{3}}{4}}$
	C. $\sqrt{\frac{2-\sqrt{3}}{2}}$
	D. $\sqrt{\frac{2-\sqrt{3}}{4}}$
	E. $\frac{\sqrt{3}}{4}$

Oplossing - Solution

$\inline 2\cdot\cos^2\alpha=1+\cos 2\alpha\\=1+\cos30^\circ=1+\frac{\sqrt{3}}{2}\\{2\cdot\cos^2\alpha=1+\cos 2\alpha}\newline{2\cdot\cos^2 15^{\circ}=1+\cos30^{\circ}}\newline{2\cdot\cos^2 15^{\circ}=1+\frac{\sqrt{3}}{2}}\newline{cos^2\,15^{\circ}=\frac{1}{2}+\frac{\sqrt{3}}{4}}\newline{cos^2\,15^{\circ}=\frac{2+\sqrt{3}}{4}}\newline{cos\;15^{\circ}=\sqrt{\frac{2+\sqrt{3}}{4}}}\newline$