Search any question & find its solution
Question:
Answered & Verified by Expert
If $\tan \mathrm{A}=\frac{1}{2}$ and $\tan \mathrm{B}=\frac{1}{3}$, then what is the value of $(\mathrm{A}+\mathrm{B})$ ?
Options:
Solution:
1138 Upvotes
Verified Answer
The correct answer is:
$\frac{\pi}{4}$
Let tan $A=\frac{1}{2}$ and $\tan B=\frac{1}{3}$
We know, $\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}$
$=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \cdot \frac{1}{3}}=\frac{\frac{5}{6}}{\frac{5}{6}}=1=\tan \pi / 4$
$\Rightarrow A+B=\pi / 4$
We know, $\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}$
$=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \cdot \frac{1}{3}}=\frac{\frac{5}{6}}{\frac{5}{6}}=1=\tan \pi / 4$
$\Rightarrow A+B=\pi / 4$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.