The value of (sec `theta` + cosec `theta`) when `theta = 45^@` is.
जब `theta= 45^@`, तो (sec`theta` + cosec `theta`) का मान क्या है?

Options

A. `5sqrt2`
B. `3sqrt2`
C. `4sqrt2`
D. `2sqrt2`

Explanation

To find the value of \( \sec \theta + \csc \theta \) when \( \theta = 45^\circ \), we can follow these steps:

### Step 1: Understand the definitions
- The secant function is defined as \( \sec \theta = \frac{1}{\cos \theta} \).
- The cosecant function is defined as \( \csc \theta = \frac{1}{\sin \theta} \).

### Step 2: Find the values of \( \sec 45^\circ \) and \( \csc 45^\circ \)
- From trigonometric tables, we know:
- \( \cos 45^\circ = \frac{1}{\sqrt{2}} \)
- \( \sin 45^\circ = \frac{1}{\sqrt{2}} \)

### Step 3: Calculate \( \sec 45^\circ \)
\[ \sec 45^\circ = \frac{1}{\cos 45^\circ} = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2} \]

### Step 4: Calculate \( \csc 45^\circ \)
\[ \csc 45^\circ = \frac{1}{\sin 45^\circ} = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2} \]

### Step 5: Add the values of \( \sec 45^\circ \) and \( \csc 45^\circ \)
\[ \sec 45^\circ + \csc 45^\circ = \sqrt{2} + \sqrt{2} = 2\sqrt{2} \]

### Conclusion
Thus, the value of \( \sec \theta + \csc \theta \) when \( \theta = 45^\circ \) is \( 2\sqrt{2} \).

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