If `tanA=1`,then find the value of `sin^(2)A+cos^(2)A+cotA`.

Answer

To solve the problem, we need to find the value of \( \sin^2 A + \cos^2 A + \cot A \) given that \( \tan A = 1 \).

### Step-by-Step Solution:

1. **Understanding the given information**:
We know that \( \tan A = 1 \). This means that the angle \( A \) is such that the opposite side and adjacent side of the triangle are equal. This occurs at \( A = 45^\circ \) or \( A = \frac{\pi}{4} \) radians.

2. **Using the Pythagorean Identity**:
We use the identity \( \sin^2 A + \cos^2 A = 1 \). This is a fundamental identity in trigonometry.

\[ \sin^2 A + \cos^2 A = 1 \]

3. **Finding \( \cot A \)**:
Since \( \tan A = 1 \), we can find \( \cot A \) using the relationship \( \cot A = \frac{1}{\tan A} \).

\[ \cot A = \frac{1}{\tan A} = \frac{1}{1} = 1 \]

4. **Substituting into the expression**:
Now we can substitute the values we found into the expression \( \sin^2 A + \cos^2 A + \cot A \).

\[ \sin^2 A + \cos^2 A + \cot A = 1 + 1 \]

5. **Calculating the final result**:
Adding these values together gives us:

\[ 1 + 1 = 2 \]

### Final Answer:
Thus, the value of \( \sin^2 A + \cos^2 A + \cot A \) is \( 2 \).

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