Question

Solve:
$\frac{\tan \theta +\sec \theta -1}{\tan \theta -\sec \theta +1}$

Answer 1

$\frac{\tan \theta +\sec \theta -1}{\tan \theta -\sec \theta +1}\frac{\tan \theta +\sec \theta -({\sec }^2\theta -{\tan }^2\theta )}{\tan \theta -\sec \theta +1}\frac{\tan \theta +\sec \theta -(\tan \theta +\sec \theta )(\sec \theta -\tan \theta )}{\tan \theta -\sec \theta +1}\frac{\tan \theta +\sec \theta (1-\sec \theta +\tan \theta )}{\tan \theta -\sec \theta +1}\tan \theta +\sec \theta \frac{\sin \theta }{\cos \theta }+\frac{1}{\cos \theta }\frac{1+\sin \theta }{\cos \theta }$