Evaluate :
`(sin 18^(@))/(cos 72^(@))`

Answer

To evaluate the expression \(\frac{\sin 18^\circ}{\cos 72^\circ}\), we can follow these steps:

### Step 1: Use the co-function identity
We know from trigonometric identities that:
\[ \sin \theta = \cos(90^\circ - \theta) \]
Applying this identity to \(\sin 18^\circ\):
\[ \sin 18^\circ = \cos(90^\circ - 18^\circ) = \cos 72^\circ \]

### Step 2: Substitute the identity into the expression
Now we can substitute \(\sin 18^\circ\) in our original expression:
\[ \frac{\sin 18^\circ}{\cos 72^\circ} = \frac{\cos 72^\circ}{\cos 72^\circ} \]

### Step 3: Simplify the expression
Since \(\cos 72^\circ\) in the numerator and denominator are the same (and not equal to zero), we can simplify:
\[ \frac{\cos 72^\circ}{\cos 72^\circ} = 1 \]

### Final Answer
Thus, the value of \(\frac{\sin 18^\circ}{\cos 72^\circ}\) is:
\[ \boxed{1} \]