| If \[\alpha +\beta =90{}^\circ \]and \[\alpha :\beta =2:1,\]then \[\tan \alpha :\tan \beta \]is equal to |
A) 1: 3
B) 3 : 2
C) 2 : 3
D) 3 : 1
Correct Answer: D
Solution :
| If \[\alpha +\beta =90{}^\circ \]and \[\alpha :\beta =2:1\] |
| Let \[\alpha =2x\]and \[\beta =x,\] respectively. |
| Then, \[2x+x=90{}^\circ \] |
| \[\Rightarrow \]\[3x=90{}^\circ \]\[\Rightarrow \]\[x=30{}^\circ \] |
| \[\therefore \] \[\alpha =2x=60{}^\circ \] |
| \[\beta =x=30{}^\circ \] |
| Hence, \[\frac{\tan \alpha }{\tan \beta }=\frac{\tan 60{}^\circ }{\tan 30{}^\circ }=\frac{\sqrt{3}}{1/\sqrt{3}}=\frac{3}{1}\] |
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