Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\frac{\sin^2\alpha +\cos^2\alpha +\tan^2\alpha}{\sin^2\alpha +\cos^2\alpha +\cot^2\alpha}$ is gelijk aan	A. tan α
	B. tan²α
	C. cot²α
	D. tan⁴α
	E. (sin²α . cos²α)⁻¹

[ 4-6765 - op net sinds 13.8.13-(E)-21.11.2024 ]

Translation in E N G L I S H

$\frac{\sin^2\alpha +\cos^2\alpha +\tan^2\alpha}{\sin^2\alpha +\cos^2\alpha +\cot^2\alpha}$ is equal to	A. tan α
	B. tan²α
	C. cot²α
	D. tan⁴α
	E. (sin²α . cos²α)⁻¹

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\sin^2\alpha+\cos^2\alpha+\tan^2\alpha}{\sin^2\alpha+\cos^2\alpha+\cot^2\alpha}=\frac{1+\tan^2\alpha}{1+\cot^2\alpha}= \frac{\frac{1}{\cos^2\alpha }}{\frac{1}{\sin^2\alpha }}=\frac{1}{\cos^2\alpha }\cdot \sin^2\alpha =\tan^2\alpha$