Question

If $\sec \theta +\tan \theta =p$ then $\sec \theta$_____

• A. $\frac{p^2}{p^2-1}$
• B. $\frac{p^2-1}{p^2+1}$
• C. $\frac{p^2+1}{p^2-1}$
• D. $\frac{p}{p^2+1}$

Answer 1

The correct option is C $\frac{p^2+1}{p^2-1}$

$\sec \theta +\tan \theta =p$------------eq1
using the formula, ${\sec \theta }^2-{\tan \theta }^2=1$
$(\sec \theta +\tan \theta )(\sec \theta -\tan \theta )=1$
$p\ast (\sec \theta -\tan \theta )=1$
$(\sec \theta -\tan \theta )=1/p$----------eq2
from eq 1 and eq2
$2\sec \theta =p+1/p$
$sec\theta =(p^2+1)/2p$
and $tan\theta =(p^2-1)/2p$
So, $Cosec\theta =sec\theta /tan\theta =(p^2+1)/(p^2-1)$
Answer (C) $\frac{p^2+1}{p^2-1}$