Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\tan(180^\circ-\alpha )}{\cos(90^\circ+\alpha )}$ is gelijk aan	A. −1
	B. cos α
	C. − cos α
	D. $\large\boldsymbol{\frac {1} {\cos\alpha} }$
	E. $\large\boldsymbol{-\,\frac {1} {\cos\alpha} }$

[ 3-1773 - op net sinds 8.11.12-(E)-3.11.2023 ]

Translation in E N G L I S H

$\frac{\tan(180^\circ-\alpha )}{\cos(90^\circ+\alpha )}$ is equal to	A. 1
	B. cos α
	C. − cos α
	D. $\boldsymbol{\frac {1} {\cos\alpha} }$
	E. $\boldsymbol{-\,\frac {1} {\cos\alpha} }$

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\tan(180^\circ-\alpha&space;)}{\cos(90^\circ+\alpha&space;)}=\frac{-\tan x}{\sin\left [90^\circ-(90^\circ+\alpha ) \right ]} =\frac{-\tan\alpha }{\sin(-\alpha )} =\frac{\tan\alpha }{\sin\alpha }=\frac{1}{\cos\alpha }$