Statement 1: The value of determinant
`|{:(sinpi,cos(x+(pi)/(4)),tan(-(pi)/(4))),(sin(x-(pi)/(4)),-cos((pi)/(2)),ln((x)/(y))),(cot((pi)/(4)+x),ln((y)/(x)),tan(pi)):}|` is zero
Statement 2: The value of skew-symetric determinant of odd order equals zero.

Answer

To solve the given problem, we need to analyze the determinant and verify the two statements provided.

### Step 1: Analyze the Determinant
We have the determinant:

\[ D = \begin{vmatrix} \sin \pi & \cos\left(x + \frac{\pi}{4}\right) & \tan\left(-\frac{\pi}{4}\right) \\ \sin\left(x - \frac{\pi}{4}\right) & -\cos\left(\frac{\pi}{2}\right) & \ln\left(\frac{x}{y}\right) \\ \cot\left(\frac{\pi}{4} + x\right) & \ln\left(\frac{y}{x}\right) & \tan(\pi) \end{vmatrix} \]

### Step 2: Simplify the Elements
1. **Evaluate the trigonometric functions:**
- \(\sin \pi = 0\)
- \(-\cos\left(\frac{\pi}{2}\right) = 0\)
- \(\tan(\pi) = 0\)
- \(\tan\left(-\frac{\pi}{4}\right) = -1\)
- \(\cot\left(\frac{\pi}{4} + x\right) = \tan\left(\frac{\pi}{2} - \left(\frac{\pi}{4} + x\right)\right) = \tan\left(\frac{\pi}{4} - x\right)\)

Thus, the determinant simplifies to:

\[ D = \begin{vmatrix} 0 & \cos\left(x + \frac{\pi}{4}\right) & -1 \\ \sin\left(x - \frac{\pi}{4}\right) & 0 & \ln\left(\frac{x}{y}\right) \\ \tan\left(\frac{\pi}{4} - x\right) & \ln\left(\frac{y}{x}\right) & 0 \end{vmatrix} \]

### Step 3: Check for Skew-Symmetry
A matrix is skew-symmetric if \(A^T = -A\). We need to check if the determinant is skew-symmetric.

1. **First Row:**
- First element is \(0\).
- Second element is \(\cos\left(x + \frac{\pi}{4}\right)\).
- Third element is \(-1\).

2. **Second Row:**
- First element is \(\sin\left(x - \frac{\pi}{4}\right)\).
- Second element is \(0\).
- Third element is \(\ln\left(\frac{x}{y}\right)\).

3. **Third Row:**
- First element is \(\tan\left(\frac{\pi}{4} - x\right)\).
- Second element is \(\ln\left(\frac{y}{x}\right)\).
- Third element is \(0\).

### Step 4: Verify Skew-Symmetry
- The first element of the first row is \(0\), which is consistent with skew-symmetry.
- The second element of the first row should equal the negative of the first element of the second row, and so forth for all elements.

After checking, we find that the determinant is indeed skew-symmetric.

### Step 5: Conclusion
Since the determinant is skew-symmetric and of odd order (3x3), we conclude that the value of the determinant is zero.

### Final Answer
- **Statement 1:** True (The value of the determinant is zero)
- **Statement 2:** True (The value of skew-symmetric determinant of odd order equals zero)