Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{1}{\tan\alpha +\cot\alpha }=$	A. $\boldsymbol{1 }$
	B. $\boldsymbol{\sin\alpha\cdot\cos\alpha }$
	C. $\boldsymbol{\tan\alpha+\cot\alpha }$
	D. $\large\boldsymbol{\frac {1} {\sin\alpha\,+\,\cos\alpha} }$
	E. $\large\boldsymbol{\frac {1} {\sin\alpha\,\cdot\,\cos\alpha} }$

(tan x = tg x = tangens x ; cot x = cotg x = cotangens x)

[ 4-2252 - op net sinds 23.12.00-(E)-2.11.2023 ]

Translation in E N G L I S H

See above

Oplossing - Solution

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

$https://latex.codecogs.com/png.image?\dpi{110}\frac{1}{\tan\alpha +\cot\alpha }=$	A. \(\boldsymbol{1 }\)
	B. \(\boldsymbol{\sin\alpha\cdot\cos\alpha }\)
	C. \(\boldsymbol{\tan\alpha+\cot\alpha }\)
	D. \(\large\boldsymbol{\frac {1} {\sin\alpha\,+\,\cos\alpha} }\)
	E. \(\large\boldsymbol{\frac {1} {\sin\alpha\,\cdot\,\cos\alpha} }\)