Mathematics

Problem

Statement-1 The value of determinant

\begin{vmatrix} \sin \pi & \cos \left( x + \frac{\pi}{4} \right) & \tan \left( x - \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} \text{ is zero.}

Statement-2 The value of skew-symmetric determinant of odd order equals zero.