Answer
$$\frac{\cos x}{\sec x}+\frac{\sin x}{\csc x}=1$$
Work Step by Step
$$A=\frac{\cos x}{\sec x}+\frac{\sin x}{\csc x}$$
- Reciprocal Identities:
$$\csc x=\frac{1}{\sin x}\hspace{2cm}\sec x=\frac{1}{\cos x}$$
So, $$\frac{\cos x}{\sec x}=\frac{\cos x}{\frac{1}{\cos x}}=\cos^2 x$$
and $$\frac{\sin x}{\csc x}=\frac{\sin x}{\frac{1}{\sin x}}=\sin^2 x$$
Apply these back to $A$:
$$A=\cos^2x+\sin^2 x$$
$$A=1$$ (Pythagorean Identity)