Wiskunde Multiple Choice Vraag

Alle oplossingen van $1+\cos x+\cos 2x=2\cos^2\frac x2$ worden gegeven door	A. $k.\pi$
	B. $k.\frac{\pi}2$
	C. $k.\frac{\pi}4$
	D. $\frac{\pi}4+k.\frac{\pi}2$
	E. $\frac{\pi}4+k.\pi$

[ 5-2160 - op net sinds 21.10.2025-(E)- ]

Translation in E N G L I S H

Determin all the solutions of $1+\cos x+\cos 2x=2\cos^2\frac x2$

Oplossing - Solution

$\inline\!1+\cos x+\cos 2x=2\cos^2\frac x2\\\Leftrightarrow\;\;2\cos^2\frac x2+\cos 2x=2\cos^2\frac x2\\\Leftrightarrow\;\cos 2x=0\\\Leftrightarrow 2x=\frac{\pi}{2}+k\pi\\\Leftrightarrow x=\frac{\pi}{4}+k\frac{\pi}2\\$