Wiskunde Multiple Choice Vraag

tan α + cot α is gelijk aan _{(x is geen veelvoud van 90° )}	A. 2. csc 2α
	B. 2. tan 2α
	C. 2. cot 2α
	D. 2. sec 2α
	E. 2. cos 2α

[ 4-7379 - op net sinds 21.10.2020-(E)-8.11.2023 ]

Translation in E N G L I S H

tan α + cot α is equal to	A. 2 ( csc 2α)
	B. 2 ( tan 2α)
	C. 2 ( cot 2α)
	D. 2 ( sec 2α)
	E. 2 ( cos 2α)

Oplossing - Solution

${\color{DarkGreen} \tan \alpha +\cot \alpha =\frac{\cos \alpha }{\sin \alpha }+\frac{\sin \alpha }{\cos \alpha }=\frac{\cos ^2\alpha +\sin ^2\alpha }{\sin \alpha \cdot \cos \alpha } } \newline {\color{DarkGreen} =\frac{2}{2\cdot \sin \alpha \cdot \cos \alpha} =\frac{2}{\sin 2\alpha }=2\cdot \csc \: 2\alpha }$