Wiskunde Multiple Choice Vraag

Wat is de maximale waarde van de breuk $\frac{40.\cos{x}.\sin^3{x}}{1+\tan^2{x}}$ ?	A. 4
	B. 5
	C. 6
	D. 8
	E. 20

[ 5-A124 - op net sinds 20.1.2026-(E)- ]

Translation in E N G L I S H

What is the maximum value of $\frac{40.\cos{x}.\sin^3{x}}{1+\tan^2{x}}$ ?

Oplossing - Solution

$\inline\\\frac{40.\cos{x}.\sin^3{x}}{1+\tan^2{x}}=\frac{40.\cos{x}.\sin^3{x}}{\frac{1}{\cos^2x}}=40.\cos^3 x.\sin^3{x}\\=5.(8\cos^3 x.\sin^3{x})=5.(2\sin x.\cos x)^2=5.\sin^2 2x$
De maximum waarde van sin² 2x is 1, dus van 5.sin³ 2x is dat 5.