Search any question & find its solution
Question:
Answered & Verified by Expert
If, \(\tan \mathrm{A}=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\), then find the value of \(\mathrm{A}+\mathrm{B}\)
Options:
Solution:
2398 Upvotes
Verified Answer
The correct answer is:
\(\frac{\pi}{4}\)
\(\begin{aligned}
& \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \cdot \frac{1}{3}}=1 \\
& \therefore A+B=45^{\circ}=\frac{\pi}{4}
\end{aligned}\)
& \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}}=1 \\
& \therefore A+B=45^{\circ}=\frac{\pi}{4}
\end{aligned}\)
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.