Question

If $sec\theta +tan\theta =p,$ then what is the value of $sec\theta -tan\theta$?

Answer 1

$\sec \theta +\tan \theta =p$
We know that ${\sec }^2\theta -{\tan }^2\theta =1$
$\Rightarrow (\sec \theta -\tan \theta )(\sec \theta +\tan \theta )=1$
$\Rightarrow (\sec \theta -\tan \theta )\left(p\right)=1$
$\Rightarrow \sec \theta -\tan \theta =\frac{1}{p}$