Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Als 1 sin x − ——— = − 3 sin x dan is 1 sin² x + ——— = sin² x	A. 6
	B. 7
	C. 8
	D. 9
	E. 11

[ 5-2159 - op net sinds 23.7.2020-(E)-3.11.2023 ]

Translation in E N G L I S H

If 1 sin x − ——— = − 3 sin x then 1 sin² x + ——— = sin² x	A. 6
	B. 7
	C. 8
	D. 9
	E. 11

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110} \sin x - \frac{1}{\sin x}=-3\\\Rightarrow \sin^2 x -2.\sin x.\frac{1}{\sin x}+\frac{1}{\sin^2 x}=9\\ \Rightarrow \sin^2 x - 2 + \frac{1}{\sin^2 x}=9\\ \Rightarrow \sin^2 x + \frac{1}{\sin^2 x} = 9+2=\cdots \\$