MCQ
If $\tan A = - \frac{1}{2}$ and $\tan B = - \frac{1}{3},$ then $A + B = $
- A$\frac{\pi }{4}$
- ✓$\frac{{3\pi }}{4}$
- C$\frac{{5\pi }}{4}$
- DNone of these
✓
Answer
Correct option: B.
$\frac{{3\pi }}{4}$
b
(b) We have $\tan A = - \frac{1}{2}$ and $\tan B = - \frac{1}{3}$
(b) 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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