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