Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\inline \LARGE \dpi{120}\frac{\sin(2\alpha\:+\:2\beta)}{\sin 2\alpha\:+\:\sin 2\beta}=$	A. $\boldsymbol{1}$
	B. $\large\boldsymbol{\frac {\sin(\alpha\,+\,\beta\,)} {\sin(\alpha\,-\,\beta\,)} }$
	C. $\large\boldsymbol{\frac {\sin(\alpha\,+\,\beta\,)} {\cos(\alpha\,-\,\beta\,)} }$
	D. $\large\boldsymbol{\frac {\cos(\alpha\,+\,\beta\,)} {\sin(\alpha\,-\,\beta\,)} }$
	E. $\large\boldsymbol{\frac {\cos(\alpha\,+\,\beta\,)} {\cos(\alpha\,-\,\beta\,)} }$

[ 5-7426 - op net sinds 27.11.13-(E)-14.11.2023 ]

Translation in E N G L I S H

See above

Oplossing - Solution

In de teller passen we de verdubbelingformule toe voor sin 2α
en in de noemer de formule van SIMPSON
$\frac{\sin(2\alpha+2\beta)}{\sin2\alpha+\sin2\beta}=\frac{\sin2(\alpha+\beta)}{\sin2\alpha+\sin2\beta)}=\frac{2\sin(\alpha+\beta).\cos(\alpha+\beta)}{2\sin(\alpha+\beta).\cos(\alpha-\beta)}=\frac{\cos(\alpha+\beta)}{\cos\alpha-\beta)}$

$https://latex.codecogs.com/png.image?\inline \LARGE \dpi{120}\frac{\sin(2\alpha\:+\:2\beta)}{\sin 2\alpha\:+\:\sin 2\beta}=$	A. \(\boldsymbol{1}\)
	B. \(\large\boldsymbol{\frac {\sin(\alpha\,+\,\beta\,)} {\sin(\alpha\,-\,\beta\,)} }\)
	C. \(\large\boldsymbol{\frac {\sin(\alpha\,+\,\beta\,)} {\cos(\alpha\,-\,\beta\,)} }\)
	D. \(\large\boldsymbol{\frac {\cos(\alpha\,+\,\beta\,)} {\sin(\alpha\,-\,\beta\,)} }\)
	E. \(\large\boldsymbol{\frac {\cos(\alpha\,+\,\beta\,)} {\cos(\alpha\,-\,\beta\,)} }\)