Quantitative Aptitude Ques 784
Question: If $ \alpha +\beta =90{}^\circ $ and $ \alpha :\beta =2:1, $ then $ \tan \alpha :\tan \beta $ is equal to
Options:
A) 1: 3
B) 3 : 2
C) 2 : 3
D) 3 : 1
Show Answer
Answer:
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} $
BETA
