Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\cot \alpha }{1+\cot^2\alpha }=$	A. \(\boldsymbol{\cos \alpha }\)
B. \(\boldsymbol{\sin\alpha\cdot\cos\alpha }\)
C. \(\large\boldsymbol{\frac {\cos \alpha} {\sin\alpha} }\)
D. \(\large\boldsymbol{\frac {\sin \alpha} {\cos\alpha}+1 }\)
E. \(\large\boldsymbol{\frac {\sin \alpha} {1\,+\,\cos\alpha} }\)

$\\{\color{DarkGreen} 1^{ste}\;manier\;: }\\ \frac{\cot\alpha }{1+\cot^2\alpha }=\frac{\cot\alpha }{\frac{1}{\sin^2\alpha }}=\cot\alpha .\sin^2\alpha =\frac{\cos\alpha }{\sin\alpha }.\sin^2\alpha =\cos\alpha .\sin\alpha \\{\color{DarkGreen} 2^{de}\;manier\;: }\\ \frac{\cot\alpha }{1+\cot^2\alpha }=\frac{\frac{\cos\alpha }{\sin\alpha }}{1+\frac{\cos^2\alpha }{\sin^2\alpha }}=\frac{\frac{\cos\alpha }{\sin\alpha }}{\frac{\sin^2\alpha +\cos^2\alpha }{\sin^2\alpha }}=\frac{\cos\alpha }{\sin\alpha }.\frac{\sin^2\alpha }{1}=\cos\alpha .\sin\alpha$