A) \[\frac{\pi }{4}\]
B) \[\frac{3\pi }{4}\]
C) \[\frac{5\pi }{4}\]
D) None of these
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, \[A+B=\frac{3\pi }{4}.\]
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