`sin18^(@)-cos72^(@)` is equal of :

Options

A. 4
B. 0
C. 2
D. 1

Answer

To solve the expression \( \sin 18^\circ - \cos 72^\circ \), we will follow these steps:

### Step 1: Rewrite \( \cos 72^\circ \)
We know from trigonometric identities that:
\[ \cos 72^\circ = \sin(90^\circ - 72^\circ) = \sin 18^\circ \]

### Step 2: Substitute \( \cos 72^\circ \) in the expression
Now we can substitute \( \cos 72^\circ \) in the original expression:
\[ \sin 18^\circ - \cos 72^\circ = \sin 18^\circ - \sin 18^\circ \]

### Step 3: Simplify the expression
Now, we simplify the expression:
\[ \sin 18^\circ - \sin 18^\circ = 0 \]

### Conclusion
Thus, the value of \( \sin 18^\circ - \cos 72^\circ \) is:
\[ \boxed{0} \]