Answer
$$1-\frac{1}{\sec^2x}=\sin^2 x$$
Work Step by Step
$$A=1-\frac{1}{\sec^2x}$$
$$A=1-\Big(\frac{1}{\sec x}\Big)^2$$
From Reciprocal Identities: $$\sec x=\frac{1}{\cos x}$$
therefore, $$\cos x=\frac{1}{\sec x}$$
so, $$\cos^2x=\Big(\frac{1}{\sec x}\Big)^2$$
That makes $A$ into $$A=1-\cos^2 x$$
$$A=\sin^2x\hspace{1cm}\text{(Pythagorean Identity)}$$
