Search any question & find its solution
Question:
Answered & Verified by Expert
A positive acute angle is divided into two parts whose
tangents are $\frac{1}{8}$ and $\frac{7}{9}$. What is the value of this angle?
Options:
tangents are $\frac{1}{8}$ and $\frac{7}{9}$. What is the value of this angle?
Solution:
1897 Upvotes
Verified Answer
The correct answer is:
$\frac{\pi}{4}$
Let two parts of an angle $\theta$ are $\phi$ and $\psi$. So, $\theta=\phi+\psi$ So, $\tan \theta=\tan (\phi+\psi)$
$=\frac{\tan \phi+\tan \psi}{1-\tan \phi \tan \psi}=\frac{\frac{1}{8}+\frac{7}{9}}{1-\frac{1}{8} \cdot \frac{7}{9}}=\frac{\frac{9+56}{72}}{\frac{72-7}{72}}=\frac{\frac{65}{72}}{\frac{65}{72}}=1$
$=\tan \frac{\pi}{4} \Rightarrow \theta=\frac{\pi}{4}$
$=\frac{\tan \phi+\tan \psi}{1-\tan \phi \tan \psi}=\frac{\frac{1}{8}+\frac{7}{9}}{1-\frac{1}{8} \cdot \frac{7}{9}}=\frac{\frac{9+56}{72}}{\frac{72-7}{72}}=\frac{\frac{65}{72}}{\frac{65}{72}}=1$
$=\tan \frac{\pi}{4} \Rightarrow \theta=\frac{\pi}{4}$
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.