Evaluate : `(tan45^(@))/(2sin30^(@)-cos60^(@))`

Answer

To evaluate the expression \(\frac{\tan 45^\circ}{2 \sin 30^\circ - \cos 60^\circ}\), we will follow these steps:

### Step 1: Find \(\tan 45^\circ\)
We know that:
\[ \tan 45^\circ = 1 \]

### Step 2: Find \(\sin 30^\circ\)
We know that:
\[ \sin 30^\circ = \frac{1}{2} \]

### Step 3: Find \(\cos 60^\circ\)
We know that:
\[ \cos 60^\circ = \frac{1}{2} \]

### Step 4: Substitute the values into the expression
Now, we substitute the known values into the expression:
\[ \frac{\tan 45^\circ}{2 \sin 30^\circ - \cos 60^\circ} = \frac{1}{2 \cdot \frac{1}{2} - \frac{1}{2}} \]

### Step 5: Simplify the denominator
Calculating the denominator:
\[ 2 \cdot \frac{1}{2} = 1 \]
So,
\[ 2 \sin 30^\circ - \cos 60^\circ = 1 - \frac{1}{2} = \frac{1}{2} \]

### Step 6: Substitute back into the expression
Now we have:
\[ \frac{1}{\frac{1}{2}} = 2 \]

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