`sin^(-1) x + cos^(-1) x = pi/4`

Answer

To solve the equation \( \sin^{-1} x + \cos^{-1} x = \frac{\pi}{4} \), we can follow these steps:

### Step 1: Understand the Inverse Trigonometric Functions
Recall that for any \( x \) in the domain of the functions, the following identity holds:
\[ \sin^{-1} x + \cos^{-1} x = \frac{\pi}{2} \]
This identity is true for all \( x \) in the interval \([-1, 1]\).

### Step 2: Analyze the Given Equation
We have:
\[ \sin^{-1} x + \cos^{-1} x = \frac{\pi}{4} \]
From the identity we established, we know that:
\[ \sin^{-1} x + \cos^{-1} x = \frac{\pi}{2} \]
This means that the left-hand side equals \( \frac{\pi}{2} \), which is not equal to \( \frac{\pi}{4} \).

### Step 3: Conclusion
Since \( \frac{\pi}{2} \neq \frac{\pi}{4} \), the original statement \( \sin^{-1} x + \cos^{-1} x = \frac{\pi}{4} \) is **false**.

### Final Answer
The statement \( \sin^{-1} x + \cos^{-1} x = \frac{\pi}{4} \) is false.

---