Question12. [T8] Algebraically solve $\frac{\sec \theta}{1+\sec \theta}=\frac{\sec ^{2} \theta}{2+\sec \theta}$ over the domain $[-\pi, \pi]$. Give exact values where possible, if not round to 2 decimal places.

Studdy Solution
Verify solutions within the domain $[- \pi, \pi]$:
The solutions $\theta = \pm \frac{\pi}{4}, \pm \frac{3\pi}{4}$ are within the domain.
The exact values of $\theta$ are:
$$\boxed{\pm \frac{\pi}{4}, \pm \frac{3\pi}{4}}$$