Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\int \frac{1}{\sin^2 x.\cos^2 x}\: dx=$	A. 2 tan 2x + C
	B. 4 tan 2x + C
	C. − cot 2x + C
	D. − 2 cot 2x + C
	E. − 4 cot 2x + C

[ 6-8736 - op net sinds 8.1.2022-(E)-15.6.2024 ]

Translation in E N G L I S H

See above

Oplossing - Solution

$\\\int\frac{1}{\sin^2 x.\cos^2 x}\:dx=\int\frac{1}{(\sin x.\cos x)^2}\:dx=\int\frac{1}{\left(\frac{\sin 2x}{2}\right)^2}\:dx=\int\frac{4}{\sin^22x}\:dx\\=2\int\frac{1}{\sin^2(2x)}\:d\:(2x)=-2\cot\,2x\:+\:C$