Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\cos x}{\sin x}-\frac{\cos 2x}{\sin 2x}$ is gelijk aan	A. − cot x
	B. csc x
	C. csc 2x
	D. cot x . csc 2x
	E. 0

[ 5-6861 - op net sinds 1.11.14-(E)-16.12.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\cos x}{\sin x}-\frac{\cos 2x}{\sin 2x}$ is equal to	A. − cot x
	B. csc x
	C. csc 2x
	D. cot x . csc 2x
	E. 0

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\\\frac{\cos x}{\sin x}-\frac{\cos 2x}{\sin 2x}= \frac{\cos x}{\sin x}-\frac{\cos^2x-\sin^2x}{2.\sin x.\cos x}=\frac{2\cos^2x-\cos^2x+\sin^2x}{2.\sin x.\cos x}\\=\frac{\cos^2x+\sin^2x}{2.\sin x.\cos x}=\frac{1}{\sin 2x}=csc 2x$