The value of expression `(1-cot23^(@))(1-cot22^(@))` is equal to :

Answer

To solve the expression \((1 - \cot 23^\circ)(1 - \cot 22^\circ)\), we can follow these steps:

### Step 1: Recognize the relationship between angles
We know that \(23^\circ + 22^\circ = 45^\circ\). Thus, we can use the identity for cotangent:
\[ \cot(45^\circ) = 1 \]
This implies:
\[ \cot(23^\circ + 22^\circ) = 1 \]

### Step 2: Use the cotangent addition formula
The cotangent addition formula states:
\[ \cot(A + B) = \frac{\cot A \cot B - 1}{\cot A + \cot B} \]
Applying this to our angles:
\[ \cot(23^\circ + 22^\circ) = \frac{\cot 23^\circ \cot 22^\circ - 1}{\cot 23^\circ + \cot 22^\circ} = 1 \]

### Step 3: Set up the equation
From the cotangent addition formula, we have:
\[ \frac{\cot 23^\circ \cot 22^\circ - 1}{\cot 23^\circ + \cot 22^\circ} = 1 \]
This implies:
\[ \cot 23^\circ \cot 22^\circ - 1 = \cot 23^\circ + \cot 22^\circ \]

### Step 4: Rearranging the equation
Rearranging gives us:
\[ \cot 23^\circ \cot 22^\circ - \cot 23^\circ - \cot 22^\circ = 1 \]

### Step 5: Adding 1 to both sides
Now, we can add 1 to both sides:
\[ \cot 23^\circ \cot 22^\circ - \cot 23^\circ - \cot 22^\circ + 1 = 2 \]

### Step 6: Factor the left-hand side
The left-hand side can be factored:
\[ (1 - \cot 23^\circ)(1 - \cot 22^\circ) = 2 \]

### Conclusion
Thus, the value of the expression \((1 - \cot 23^\circ)(1 - \cot 22^\circ)\) is:
\[ \boxed{2} \]

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