Quantitative Aptitude Ques 2143
Question: If $ (1+\tan A)(1+\tan B)=2, $ then $ (A+B) $ is equal to
Options:
A) $ \frac{\pi }{2} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{4} $
D) $ \frac{\pi }{6} $
E) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ 1+\tan A+\tan B+\tan A\tan B=2 $
$ \Rightarrow $ $ \tan A+\tan B=1-\tan A\tan B $
$ \Rightarrow $ $ \frac{\tan A+\tan B}{1-\tan AtanB}=1=\tan 45{}^\circ $
$ \Rightarrow $ $ \tan (A+B)=\tan 45{}^\circ $ $ [ \because \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B} ] $
$ \therefore $ $ A+B=45{}^\circ =\frac{\pi }{4} $
BETA
