What is the value of `(sin theta)/(cosec theta)+(cos theta)/(sec theta)` ?

Options

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

Answer

To find the value of \((\sin \theta)/(\csc \theta) + (\cos \theta)/(\sec \theta)\), we can follow these steps:

### Step 1: Rewrite the trigonometric functions
We know that:
- \(\csc \theta = \frac{1}{\sin \theta}\)
- \(\sec \theta = \frac{1}{\cos \theta}\)

So we can rewrite the expression:
\[ \frac{\sin \theta}{\csc \theta} + \frac{\cos \theta}{\sec \theta} = \frac{\sin \theta}{\frac{1}{\sin \theta}} + \frac{\cos \theta}{\frac{1}{\cos \theta}} \]

### Step 2: Simplify the fractions
Now, simplify each term:
\[ \frac{\sin \theta}{\frac{1}{\sin \theta}} = \sin^2 \theta \]
\[ \frac{\cos \theta}{\frac{1}{\cos \theta}} = \cos^2 \theta \]

So we can now rewrite the expression as:
\[ \sin^2 \theta + \cos^2 \theta \]

### Step 3: Use the Pythagorean identity
We know from trigonometric identities that:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]

### Final Answer
Thus, the value of \((\sin \theta)/(\csc \theta) + (\cos \theta)/(\sec \theta)\) is:
\[ \boxed{1} \]