1. Tardigrade
  2. Question
  3. Mathematics
  4. For 0 le P,Q le (π/2), if sin P + cos Q=2, then the value of tan ((P + Q/2)) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. For $0 \le P,Q \le \frac{\pi}{2}$, if sin P + cos $Q=2$, then the value of tan $\left(\frac{P + Q}{2}\right)$ is equal to

WBJEEWBJEE 2013

Solution:

Given, $0 \leq P, Q \leq \frac{\pi}{2}$
and $\sin P+\cos Q=2$ ..... (i)
This equation hold only when, $\quad P=\frac{\pi}{2}$
and $Q=0$
$LHS =\sin P+\cos Q=\sin \frac{\pi}{2}+\cos 0$
$=1+1=2= RHS$
$\therefore \tan \left(\frac{P+Q}{2}\right)=\tan \left(\frac{\frac{\pi}{2}+0}{2}\right)=\tan \frac{\pi}{4}=1$