If `sinx=cosy`, write the relation between x and y, if both the angles x and y are acute.

Answer

To solve the problem, we need to find the relation between the angles \( x \) and \( y \) given that \( \sin x = \cos y \) and both angles are acute.

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ \sin x = \cos y \]

2. **Use the co-function identity:**
We know from trigonometric identities that:
\[ \cos y = \sin(90^\circ - y) \]
Therefore, we can rewrite the equation as:
\[ \sin x = \sin(90^\circ - y) \]

3. **Apply the property of sine function:**
Since both \( x \) and \( 90^\circ - y \) are acute angles (between \( 0^\circ \) and \( 90^\circ \)), we can equate the angles:
\[ x = 90^\circ - y \]

4. **Rearranging the equation:**
To express the relationship between \( x \) and \( y \), we can rearrange the equation:
\[ x + y = 90^\circ \]

### Final Relation:
Thus, the relation between \( x \) and \( y \) is:
\[ x + y = 90^\circ \]