`sin^(2) 60^(@) + 2 tan 45^(@) - cos^(2) 30^(@)`

Answer

To solve the expression \( \sin^2 60^\circ + 2 \tan 45^\circ - \cos^2 30^\circ \), we will follow these steps:

### Step 1: Calculate \( \sin^2 60^\circ \)
We know that:
\[ \sin 60^\circ = \frac{\sqrt{3}}{2} \]
Thus,
\[ \sin^2 60^\circ = \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{3}{4} \]

### Step 2: Calculate \( \tan 45^\circ \)
We know that:
\[ \tan 45^\circ = 1 \]
Therefore,
\[ 2 \tan 45^\circ = 2 \times 1 = 2 \]

### Step 3: Calculate \( \cos^2 30^\circ \)
We know that:
\[ \cos 30^\circ = \frac{\sqrt{3}}{2} \]
Thus,
\[ \cos^2 30^\circ = \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{3}{4} \]

### Step 4: Combine all the values
Now substituting these values into the original expression:
\[ \sin^2 60^\circ + 2 \tan 45^\circ - \cos^2 30^\circ = \frac{3}{4} + 2 - \frac{3}{4} \]

### Step 5: Simplify the expression
The \( \frac{3}{4} \) and \( -\frac{3}{4} \) will cancel each other out:
\[ \frac{3}{4} - \frac{3}{4} + 2 = 0 + 2 = 2 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{2} \]

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