The least value of `cos theta + sin theta` is

Answer

To find the least value of \( \cos \theta + \sin \theta \), we can use the formula for the minimum value of the expression \( A \cos \theta + B \sin \theta \), which is given by:

\[ -\sqrt{A^2 + B^2} \]

### Step-by-Step Solution:

1. **Identify A and B**:
In the expression \( \cos \theta + \sin \theta \), we can identify:
- \( A = 1 \) (coefficient of \( \cos \theta \))
- \( B = 1 \) (coefficient of \( \sin \theta \))

2. **Apply the formula for the least value**:
Using the formula for the least value:
\[ \text{Least Value} = -\sqrt{A^2 + B^2} \]
Substitute \( A \) and \( B \):
\[ \text{Least Value} = -\sqrt{1^2 + 1^2} \]

3. **Calculate \( A^2 + B^2 \)**:
\[ A^2 + B^2 = 1^2 + 1^2 = 1 + 1 = 2 \]

4. **Find the square root**:
\[ \sqrt{2} \]

5. **Substitute back into the least value formula**:
\[ \text{Least Value} = -\sqrt{2} \]

Thus, the least value of \( \cos \theta + \sin \theta \) is \( -\sqrt{2} \).

### Final Answer:
The least value of \( \cos \theta + \sin \theta \) is \( -\sqrt{2} \).

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