Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac {1+\tan \alpha } {1+\cot \beta }$ is gelijk aan	A. 1
B. tan α
C. tan² α
D. cot α
E. cot² α

$\frac {1+\tan \alpha } {1+\cot \beta }$ is equal to	A. 1
B. tan α
C. tan² α
D. cot α
E. cot² α

1^ste manier :
$\\\frac{1\!+\!\tan\alpha}{1\!+\!\cot\beta}\!=\!\frac{1\!+\!\frac{\sin\alpha}{\cos\alpha}}{1\!+\!\frac{\cos\alpha}{\sin\alpha}}\!=\!\frac{\frac{\cos\alpha+\sin\alpha}{\cos\alpha}}{\frac{\sin\alpha+\cos\alpha}{\sin\alpha}}\!=\!\frac{\cos\alpha+\sin\alpha}{\cos\alpha}.\frac{\sin\alpha}{\sin\alpha+\cos\alpha}\!=\!\frac{\sin\alpha}{\cos\alpha}\!=\!\tan\alpha$
2^de manier :
$\\ \frac{1\!+\!\tan\alpha}{1\!+\!\cot\alpha} =\frac{1+\tan\alpha}{1+\frac{1}{\tan\alpha}} =\frac{1+\tan\alpha}{\frac{\tan\alpha+1}{\tan\alpha}} =(1+\tan\alpha).\frac{\tan\alpha}{\tan\alpha+1} =\tan\alpha$