If sec $\theta +\text{tan} \theta$ = s, then find the value of $\frac{s^2 -1}{s^2 +1}$

Given:
$s = \sec\theta + \tan\theta$

Use identity:
$(\sec\theta + \tan\theta)(\sec\theta - \tan\theta) = 1$

So,
$\sec\theta - \tan\theta = \frac{1}{s}$

Now,
Add and subtract:
$2\sec\theta = s + \frac{1}{s}$
$2\tan\theta = s - \frac{1}{s}$

We need:
$\frac{s^2 - 1}{s^2 + 1}$

Divide numerator and denominator by $s$:
$\frac{s - \frac{1}{s}}{s + \frac{1}{s}}$

Substitute:
$= \frac{2\tan\theta}{2\sec\theta}$
$= \frac{\tan\theta}{\sec\theta}$

$= \sin\theta$

Correct Answer: $\sin\theta$