Question

Given that x = $sec\theta$ + $tan\theta$ , y = $sec\theta -$ $tan\theta$ . Establish a relation between x and y by eliminating '$\theta$' .

Answer 1

Given that $x=\text{sec}\theta +\tan \theta$

$y=\text{sec}\theta -\tan \theta$

As we know that

${\text{sec}}^2\theta -{\tan }^2\theta =1$

$⟹(\text{sec}\theta +\tan \theta )(\text{sec}\theta -\tan \theta )=1$

$⟹xy=1$