Answer
$$\sec^2\theta-\tan^2\theta=1$$
Work Step by Step
$$A=\sec^2\theta-\tan^2\theta$$
We need to use 2 identities here, which are
$$\sec\theta=\frac{1}{\cos\theta}\hspace{2cm}\tan\theta=\frac{\sin\theta}{\cos\theta}$$
Therefore, $A$ would be
$$A=\frac{1}{\cos^2\theta}-\frac{\sin^2\theta}{\cos^2\theta}$$
$$A=\frac{1-\sin^2\theta}{\cos^2\theta}$$
Recall that $1-\sin^2\theta=\cos^2\theta$ from Pythagorean identities.
$$A=\frac{\cos^2\theta}{\cos^2\theta}$$
$$A=1$$
