Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}1\, -\, \frac{\sin^2\alpha }{1-\cos\alpha }$ is gelijk aan	A. cos α
	B. − cos α
	C. 1 − sin α
	D. − sin² α
	E. sin α . cos α

[ 4-6176 - op net sinds 4.6.2020-(E)-8.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}1\, -\, \frac{\sin^2\alpha }{1-\cos\alpha }$ is equal to	A. cos α
	B. − cos α
	C. 1 − sin α
	D. − sin² α
	E. (sin α )( cos α)

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\\1\, -\, \frac{\sin^2\alpha }{1-\cos\alpha } =1\, -\, \frac{1-\cos^2\alpha }{1-\cos\alpha } =1\, -\, \frac{(1-\cos\alpha)(1+\cos\alpha ) }{1-\cos\alpha }\\{\color{Green} .}\qquad\qquad\qquad =1-(1+\cos\alpha ) =1-1-\cos\alpha = -\cos\alpha$