Evaluate `sinthetacos(90^(@)-theta)+costhetasin(90^(@)-theta)`.

Answer

To evaluate the expression \( \sin \theta \cos(90^\circ - \theta) + \cos \theta \sin(90^\circ - \theta) \), we can follow these steps:

### Step 1: Use the co-function 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
Now, we can substitute these identities into the original 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
According to the Pythagorean identity, we know that:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]

### Final Result
Thus, the value of the expression \( \sin \theta \cos(90^\circ - \theta) + \cos \theta \sin(90^\circ - \theta) \) is:
\[ \boxed{1} \]

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