Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\sin \alpha}{1+\cos\alpha}=$	A. $\boldsymbol{\tan\frac{\alpha}{2}}$
	B. $\boldsymbol{2\,\tan \frac{\alpha}{2}}$
	C. $\boldsymbol{\cot\frac{\alpha}{2}}$
	D. $\boldsymbol{2\,\cot\frac{\alpha}{2}}$
	E. $\boldsymbol{1+\tan\alpha}$

[ ?-7981 - op net sinds 4.10.2022-(E)-2.12.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\sin \alpha}{1+\cos\alpha}=$	A. $\boldsymbol{\tan \frac{\alpha}{2}}$
	B. $\boldsymbol{2\,\tan \frac{\alpha}{2}}$
	C. $\boldsymbol{\cot \frac{\alpha}{2}}$
	D. $\boldsymbol{2\,\cot \frac{\alpha}{2}}$
	E. $\boldsymbol{1+\tan\alpha}$

Oplossing - Solution

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

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\sin \alpha}{1+\cos\alpha}=$	A. \(\boldsymbol{\tan\frac{\alpha}{2}}\)
	B. \(\boldsymbol{2\,\tan \frac{\alpha}{2}}\)
	C. \(\boldsymbol{\cot\frac{\alpha}{2}}\)
	D. \(\boldsymbol{2\,\cot\frac{\alpha}{2}}\)
	E. \(\boldsymbol{1+\tan\alpha}\)

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\sin \alpha}{1+\cos\alpha}=$	A. \(\boldsymbol{\tan \frac{\alpha}{2}}\)
	B. \(\boldsymbol{2\,\tan \frac{\alpha}{2}}\)
	C. \(\boldsymbol{\cot \frac{\alpha}{2}}\)
	D. \(\boldsymbol{2\,\cot \frac{\alpha}{2}}\)
	E. \(\boldsymbol{1+\tan\alpha}\)