Find the value of `(sin45^(@) + cos 45^(@))`

Answer

To find the value of \( \sin 45^\circ + \cos 45^\circ \), we can follow these steps:

### Step 1: Find the values of \( \sin 45^\circ \) and \( \cos 45^\circ \)
We know that:
\[ \sin 45^\circ = \frac{1}{\sqrt{2}} \]
\[ \cos 45^\circ = \frac{1}{\sqrt{2}} \]

### Step 2: Add the values together
Now, we can add these two values:
\[ \sin 45^\circ + \cos 45^\circ = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} \]

### Step 3: Simplify the expression
Since both terms are the same, we can combine them:
\[ \sin 45^\circ + \cos 45^\circ = \frac{1 + 1}{\sqrt{2}} = \frac{2}{\sqrt{2}} \]

### Step 4: Rationalize the denominator
To simplify \( \frac{2}{\sqrt{2}} \), we multiply the numerator and the denominator by \( \sqrt{2} \):
\[ \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2} \]

### Final Answer
Thus, the value of \( \sin 45^\circ + \cos 45^\circ \) is:
\[ \sqrt{2} \]

---