Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\frac {2\cot \alpha} {1\,+\,\cot^2 \alpha}$ is gelijk aan	A. sin 2α
	B. cos 2α
	C. cot 2α
	D. 2 sin α
	E. 2 sin α . sin α + cos α

[ 5-3409 - op net sinds 9.9.13-(E)-25.10.2023 ]

Translation in E N G L I S H

$\frac {2\cot \alpha} {1\,+\,\cot^2 \alpha}$ is equal to	A. sin 2α
	B. cos 2α
	C. cot 2α
	D. 2 sin α
	E. 2 sin α . sin α + cos α

Oplossing - Solution

$\frac {2\cot \alpha} {1\,+\,\cot^2 \alpha}=\frac {2\cot \alpha} {\frac{1}{\sin^2 \alpha}}=2\cdot \frac{\cos \alpha}{\sin \alpha} \cdot \sin^2 \alpha=2.\cos \alpha \cdot \sin \alpha =\sin 2\alpha$