Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Hoeveel van de volgende vier uitdrukkingen zijn gelijk aan 1 ? ( α ≠ k. )	$https://latex.codecogs.com/png.image?\large \dpi{110}\\\frac{1}{\cos^2\alpha}-\tan^2\alpha\\\\\frac{1}{\sin^2\alpha}-\cot^2\alpha\\ \tan^2\alpha+\cot^2\alpha\\\tan\alpha\cdot\cot\alpha$	A. 1
		B. 2
		C. 3
		D. 4
		E. 0

[ 4-0525 - op net sinds 28.7.12-(E)-3.11.2023 ]

Translation in E N G L I S H

How many of these four expressions are equal to 1 ? ( α ≠ k. )	$https://latex.codecogs.com/png.image?\large \dpi{110}\\\frac{1}{\cos^2\alpha}-\tan^2\alpha\\\\\frac{1}{\sin^2\alpha}-\cot^2\alpha\\ \tan^2\alpha+\cot^2\alpha\\\tan\alpha\cdot\cot\alpha$	A. 1
		B. 2
		C. 3
		D. 4
		E. 0

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}<<\frac{1}{\cos^2\alpha }-\tan^2\alpha =\frac{1-\sin^2\alpha }{\cos^2\alpha }=\frac{\cos^2\alpha }{\cos^2\alpha }=1 \\{\color{Green} .}\\\frac{1}{\sin^2\alpha }-\cot^2\alpha =\frac{1-\cos^2\alpha }{\sin^2\alpha }=\frac{\sin^2\alpha }{\sin^2\alpha }=1\\ {\color{Green} .}\\\tan^2 45^\circ + \cot^2 45^\circ=1^2+1^2=2\\{\color{Green} .}\\\tan\alpha .\cot\alpha =\frac{\sin\alpha }{\cos\alpha } .\frac{\cos\alpha }{\sin\alpha }=1$