Step 1 :Given the expression \(\frac{\cos \theta}{\sec \theta}+\frac{\sin \theta}{\csc \theta}\)
Step 2 :Recall that the secant of an angle in a right triangle is the reciprocal of the cosine function, and the cosecant of an angle is the reciprocal of the sine function.
Step 3 :Therefore, we can rewrite the given expression as \(\cos \theta \cdot \cos \theta + \sin \theta \cdot \sin \theta\)
Step 4 :Which simplifies to \(\sin^2(\theta) + \cos^2(\theta)\)
Step 5 :According to the Pythagorean identity in trigonometry, \(\sin^2(\theta) + \cos^2(\theta) = 1\)
Step 6 :Final Answer: \(\boxed{1}\)