Find the value of the following expression:
`sin(sin^(-1)x+cos^(-1)x),|x|,le1`

Explanation

To find the value of the expression \( \sin(\sin^{-1}x + \cos^{-1}x) \) for \( |x| \leq 1 \), we can follow these steps:

### Step 1: Define the Variables
Let:
- \( a = \sin^{-1}x \)
- \( b = \cos^{-1}x \)

### Step 2: Use the Definitions of Inverse Functions
From the definitions:
- \( \sin a = x \)
- \( \cos b = x \)

### Step 3: Use the Pythagorean Identity
We know that:
- \( \cos a = \sqrt{1 - \sin^2 a} = \sqrt{1 - x^2} \)
- \( \sin b = \sqrt{1 - \cos^2 b} = \sqrt{1 - x^2} \)

### Step 4: Apply the Sine Addition Formula
We need to find \( \sin(a + b) \). Using the sine addition formula:
\[ \sin(a + b) = \sin a \cos b + \cos a \sin b \]

### Step 5: Substitute the Values
Substituting the values we found:
- \( \sin a = x \)
- \( \cos b = x \)
- \( \cos a = \sqrt{1 - x^2} \)
- \( \sin b = \sqrt{1 - x^2} \)

Thus, we have:
\[ \sin(a + b) = x \cdot x + \sqrt{1 - x^2} \cdot \sqrt{1 - x^2} \]
This simplifies to:
\[ \sin(a + b) = x^2 + (1 - x^2) \]

### Step 6: Simplify the Expression
Now, simplifying the expression:
\[ \sin(a + b) = x^2 + 1 - x^2 = 1 \]

### Conclusion
Therefore, the value of the expression \( \sin(\sin^{-1}x + \cos^{-1}x) \) is:
\[ \boxed{1} \]