Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\sin x + \sin y}{\cos x + \cos y}$ is gelijk aan	A. tan (x + y)
	B. 2 tan (x + y)
	C. tan (x − y)
	D. tan (x + y)
	E. tan x + tan y

[ 5-3645 - op net sinds 11.1.16-(E)-4.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\sin x + \sin y}{\cos x + \cos y}$ is equal to	A. tan ((x + y))
	B. 2 tan ((x + y))
	C. tan ((x − y))
	D. tan (x + y)
	E. tan x + tan y

Oplossing - Solution

$\frac{\sin x+\sin y}{\cos x+\cos y}\overset{Simpson}{=}\frac{2\sin\frac{x+y}{2}.\cos\frac{x-y}{2}}{2\cos\frac{x+y}{2}.\cos\frac{x-y}{2}}=\tan\frac{x+y}{2}$