The maximum value of `Delta=|(1,1,1),(1,1+sintheta,1),(1+costheta,1,1)|` is (`theta` is real) (A) `1/2` (B) `(sqrt(3))/2` (C) `sqrt(2)` (D) `-(sqrt(3))/2`

Explanation

To find the maximum value of the determinant \( \Delta = \left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1 + \sin \theta & 1 \\ 1 + \cos \theta & 1 & 1 \end{array} \right| \), we will calculate the determinant step by step.

### Step 1: Write the Determinant
We start with the determinant:

\[ \Delta = \left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1 + \sin \theta & 1 \\ 1 + \cos \theta & 1 & 1 \end{array} \right| \]
...