Find the Values of `(sin36^(@))/(cos54^(@))*`

Answer

To find the value of \(\frac{\sin 36^\circ}{\cos 54^\circ}\), we can use the relationship between sine and cosine.

### Step 1: Recognize the relationship between sine and cosine
We know that:
\[ \sin \theta = \cos (90^\circ - \theta) \]
Using this property, we can rewrite \(\sin 36^\circ\).

### Step 2: Rewrite \(\sin 36^\circ\) using cosine
Using the relationship:
\[ \sin 36^\circ = \cos (90^\circ - 36^\circ) = \cos 54^\circ \]

### Step 3: Substitute the value in the expression
Now we can substitute \(\sin 36^\circ\) in our original expression:
\[ \frac{\sin 36^\circ}{\cos 54^\circ} = \frac{\cos 54^\circ}{\cos 54^\circ} \]

### Step 4: Simplify the expression
Since \(\cos 54^\circ\) in the numerator and denominator are the same, we can simplify:
\[ \frac{\cos 54^\circ}{\cos 54^\circ} = 1 \]

### Final Answer
Thus, the value of \(\frac{\sin 36^\circ}{\cos 54^\circ}\) is:
\[ \boxed{1} \]