What is `(sintheta)/("cosec "theta)+(costheta)/(sectheta)` equal to ?

Options

A. 1
B. `(1)/(2)`
C. `(1)/(3)`
D. 2

Explanation

To solve the expression \(\frac{\sin \theta}{\csc \theta} + \frac{\cos \theta}{\sec \theta}\), we will follow these steps:

### Step 1: Rewrite the expression using trigonometric identities
We know that \(\csc \theta = \frac{1}{\sin \theta}\) and \(\sec \theta = \frac{1}{\cos \theta}\). Therefore, we can rewrite the expression as:

\[ \frac{\sin \theta}{\csc \theta} = \frac{\sin \theta}{\frac{1}{\sin \theta}} = \sin^2 \theta \]

and

\[ \frac{\cos \theta}{\sec \theta} = \frac{\cos \theta}{\frac{1}{\cos \theta}} = \cos^2 \theta \]

### Step 2: Combine the rewritten terms
Now, we can combine the two results:

\[ \sin^2 \theta + \cos^2 \theta \]

### Step 3: Use the Pythagorean identity
According to the Pythagorean identity, we know that:

\[ \sin^2 \theta + \cos^2 \theta = 1 \]

### Final Result
Thus, the original expression simplifies to:

\[ \frac{\sin \theta}{\csc \theta} + \frac{\cos \theta}{\sec \theta} = 1 \]