Find the value of `sin50^(@)-cos40^(@)`.

Answer

To find the value of \( \sin 50^\circ - \cos 40^\circ \), we can use the trigonometric identity that relates sine and cosine.

### Step-by-step Solution:

1. **Recognize the relationship between sine and cosine:**
We know that \( \cos(90^\circ - \theta) = \sin(\theta) \).

2. **Rewrite \( \cos 40^\circ \):**
We can express \( \cos 40^\circ \) using the identity:
\[ \cos 40^\circ = \cos(90^\circ - 50^\circ) = \sin 50^\circ \]

3. **Substitute into the original expression:**
Now we can substitute \( \cos 40^\circ \) in our original expression:
\[ \sin 50^\circ - \cos 40^\circ = \sin 50^\circ - \sin 50^\circ \]

4. **Simplify the expression:**
This simplifies to:
\[ \sin 50^\circ - \sin 50^\circ = 0 \]

### Final Answer:
Thus, the value of \( \sin 50^\circ - \cos 40^\circ \) is \( 0 \).