Perform the indicated operation and simplify the result.
\[
\frac{\cos \theta}{\sec \theta}+\frac{\sin \theta}{\csc \theta}
\]
What does $\frac{\cos \theta}{\sec \theta}+\frac{\sin \theta}{\csc \theta}$ equal?
A. $2 \sin \theta \cos \theta$
B. $\sin \theta+\cos \theta$
C. $\csc \theta$
D. 1
E. $\sec \theta$
F. 0
Answer
Final Answer: \(\boxed{1}\)
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: \(\boxed{1}\)
