Find the value of `(tan60^(@))/(sin30^(@)+cos60^(@))`

Answer

To solve the expression \(\frac{\tan 60^\circ}{\sin 30^\circ + \cos 60^\circ}\), we will follow these steps:

### Step 1: Find the value of \(\tan 60^\circ\)
We know from trigonometric ratios that:
\[ \tan 60^\circ = \sqrt{3} \]

### Step 2: Find the value of \(\sin 30^\circ\)
From trigonometric values, we have:
\[ \sin 30^\circ = \frac{1}{2} \]

### Step 3: Find the value of \(\cos 60^\circ\)
Similarly, we know that:
\[ \cos 60^\circ = \frac{1}{2} \]

### Step 4: Substitute the values into the expression
Now we can substitute the values we found into the original expression:
\[ \frac{\tan 60^\circ}{\sin 30^\circ + \cos 60^\circ} = \frac{\sqrt{3}}{\frac{1}{2} + \frac{1}{2}} \]

### Step 5: Simplify the denominator
The denominator simplifies as follows:
\[ \frac{1}{2} + \frac{1}{2} = 1 \]

### Step 6: Final calculation
Now substituting back into the expression gives:
\[ \frac{\sqrt{3}}{1} = \sqrt{3} \]

### Final Answer
Thus, the value of \(\frac{\tan 60^\circ}{\sin 30^\circ + \cos 60^\circ}\) is:
\[ \sqrt{3} \]