Answer
$$\sec^2 x-1=\frac{\sin^2 x}{\cos^2 x}$$
$\text{A}$ is the answer.
Work Step by Step
$$A=\sec^2 x-1$$
A Pythagorean Identity related to $\sec^2\theta$ states that $$\sec^2\theta=\tan^2\theta+1$$
That means we can rewrite $A$ as follows:
$$A=\tan^2 x+1-1$$
$$A=\tan^2 x$$
Also, from Quotient Identities, we know
$$\tan\theta=\frac{\sin\theta}{\cos\theta}$$
Therefore, $$A=\Bigg(\frac{\sin x}{\cos x}\Bigg)^2$$
$$A=\frac{\sin^2 x}{\cos^2 x}$$
$\text{A}$ is the answer.
