Wiskunde Multiple Choice Vraag

cot 2α + csc 2α α is gelijk aan	A. sin α
B. cos α
C. tan α
D. cos α
E. sec α

$\inline\\\cot 2\alpha+\csc2\alpha=\frac{1}{\tan 2\alpha}+\frac{1}{\sin 2\alpha}=\frac{1-\tan^2\alpha}{2\tan{\alpha}}+\frac{1}{2\sin{\alpha}\cos{\alpha}}\\=\frac{(1-\tan^2\alpha)\cos\alpha}{2\sin\alpha}+\frac{1}{2\sin\alpha.\cos\alpha}=\frac{(1-\tan^2\alpha)\cos^2\alpha+1}{2\sin\alpha\cos\alpha\alpha}\\=\frac{\cos^2\alpha-\sin^2\alpha+1}{2\sin\alpha\cos\alpha}=\frac{2\cos^2\alpha}{2\sin\alpha\cos\alpha}=\frac{\cos\alpha}{\sin\alpha}=\cot\alpha$