Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$-\sin^4\frac{\pi}{4}-\cos^4\frac{\pi}{4}$ is gelijk aan	A. −2
	B. −1
	C. 0
	D. − 4
	E. − 0,5

[ 5-0647 - op net sinds 12.3.2020-(E)-13.6.2025 ]

Translation in E N G L I S H

$-\sin^4\frac{\pi}{4}-\cos^4\frac{\pi}{4}$ is equal to	A. − 2
	B. − 1
	C. 0
	D. − 4
	E. − 0.5

Oplossing - Solution

$-\sin^4\frac{\pi}{4}\,-\,\cos^4\frac{\pi}{4}=-2.\sin^4\frac{\pi}{4}=-2\left(\frac{\sqrt2}{2}\right)^4=-2.\frac{\sqrt2}{2}.\frac{\sqrt2}{2}.\frac{\sqrt2}{2}.\frac{\sqrt2}{2}=-\frac{2.2.2}{16}=-\frac{8}{16}=-\frac12$