Range of the function `f(x)=|sinx|cosx|+cosx|sinx||`is `[a,b]` then `(a+b)` is equal to

Explanation

To find the range of the function \( f(x) = |\sin x| \cdot |\cos x| + |\cos x| \cdot |\sin x| \), we can simplify this expression step by step.

### Step 1: Simplify the function
The function can be rewritten as:
\[ f(x) = 2 |\sin x| |\cos x| \]
This is because both terms in the original function are identical.

### Step 2: Use the double angle identity
We know that:
\[ |\sin x| |\cos x| = \frac{1}{2} |\sin(2x)| \]
Thus, we can rewrite \( f(x) \) as:
\[ f(x) = 2 \cdot \frac{1}{2} |\sin(2x)| = |\sin(2x)| \]

### Step 3: Determine the range of \( |\sin(2x)| \)
The function \( |\sin(2x)| \) oscillates between 0 and 1 for all values of \( x \). Therefore, the range of \( f(x) \) is:
\[ [0, 1] \]

### Step 4: Identify the values of \( a \) and \( b \)
From the range \( [0, 1] \), we can identify:
- \( a = 0 \)
- \( b = 1 \)

### Step 5: Calculate \( a + b \)
Now we can compute:
\[ a + b = 0 + 1 = 1 \]

Thus, the final answer is:
\[ \boxed{1} \]