Search any question & find its solution
Question:
Answered & Verified by Expert
In a triangle $\mathrm{PQR}, \angle \mathrm{R}=\pi / 2$. If $\tan \left(\frac{\mathrm{p}}{2}\right)$ and $\tan \left(\frac{\mathrm{Q}}{2}\right)$ are roots of $\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0$, where $\mathrm{a} \neq 0$, then which one is true ?
Options:
Solution:
1144 Upvotes
Verified Answer
The correct answer is:
$c=a+b$
Hints: $\frac{\mathrm{P}}{2}+\frac{\mathrm{Q}}{2}=\frac{\pi}{2}-\frac{\mathrm{P}}{2}=\frac{\pi}{2}-\frac{\pi}{4}=\frac{\pi}{4}$
$$
\begin{aligned}
& \tan \left(\frac{\rho}{2}+\frac{Q}{2}\right)=1, \frac{-b / a}{1-c / a}=1 \Rightarrow \frac{-b}{a-c}=1 \\
& -b=a-c \Rightarrow a+b=c
\end{aligned}
$$
$$
\begin{aligned}
& \tan \left(\frac{\rho}{2}+\frac{Q}{2}\right)=1, \frac{-b / a}{1-c / a}=1 \Rightarrow \frac{-b}{a-c}=1 \\
& -b=a-c \Rightarrow a+b=c
\end{aligned}
$$
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.