Trigonometric Identities Question 366
Question: If $ \tan A=-\frac{1}{2} $ and $ \tan B=-\frac{1}{3}, $ then $ A+B= $
[IIT 1967; MNR 1987; MP PET 1989]
Options:
A) $ \frac{\pi }{4} $
B) $ \frac{3\pi }{4} $
C) $ \frac{5\pi }{4} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ \tan A=-\frac{1}{2} $ and $ \tan B=-\frac{1}{3} $ Now, $ \tan ,(A+B)=\frac{\tan A+\tan B}{1-\tan A,\tan B}=\frac{-\frac{1}{2}-\frac{1}{3}}{1-\frac{1}{2}.\frac{1}{3}}=-1 $
$ \Rightarrow \tan ,(A+B)=\tan \frac{3\pi }{4}. $ Hence, $ A+B=\frac{3\pi }{4}. $
BETA
