Write the value of `sintheta cos(90^(@)-theta)+costheta sin(90^(@)-theta).`

Explanation

To solve the expression \( \sin \theta \cos(90^\circ - \theta) + \cos \theta \sin(90^\circ - \theta) \), we can use trigonometric identities. Let's break it down step by step.

### Step 1: Identify the Trigonometric Identities
We know from trigonometric identities that:
- \( \cos(90^\circ - \theta) = \sin \theta \)
- \( \sin(90^\circ - \theta) = \cos \theta \)

### Step 2: Substitute the Identities into the Expression
Using the identities, we can rewrite the expression:
\[ \sin \theta \cos(90^\circ - \theta) + \cos \theta \sin(90^\circ - \theta) = \sin \theta \sin \theta + \cos \theta \cos \theta \]

### Step 3: Simplify the Expression
This simplifies to:
\[ \sin^2 \theta + \cos^2 \theta \]

### Step 4: Apply the Pythagorean Identity
We know from the Pythagorean identity that:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]

### Final Answer
Thus, the value of the original expression is:
\[ \boxed{1} \]

---