What is the value of `(2+tan60^(@))` ?

Options

A. 3
B. `(2)/(sqrt(3))`
C. `(4)/(sqrt(3))`
D. `2+sqrt(3)`

Answer

To find the value of \(2 + \tan 60^\circ\), we can follow these steps:

### Step 1: Identify the value of \(\tan 60^\circ\)
The tangent of \(60^\circ\) is a well-known trigonometric value. We can recall that:
\[ \tan 60^\circ = \sqrt{3} \]

### Step 2: Substitute \(\tan 60^\circ\) into the expression
Now that we know \(\tan 60^\circ\), we can substitute it into the expression:
\[ 2 + \tan 60^\circ = 2 + \sqrt{3} \]

### Step 3: Write the final answer
Thus, the value of \(2 + \tan 60^\circ\) is:
\[ 2 + \sqrt{3} \]

### Conclusion
The correct answer from the provided options is:
\[ \text{Option 4: } 2 + \sqrt{3} \]

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