Without expanding, show that the value of each of the determinants is zero: `|"cos"(x+y) \-sin(x+y) \cos2y\ sinx\ cosx\ siny\ -cosx \ sinx \ -cosy|`

Explanation

To show that the value of the given determinant is zero without expanding, we can use properties of determinants and row operations. Let's denote the determinant as \( D \):

\[
D = \begin{vmatrix}
\cos(x+y) & -\sin(x+y) & \cos(2y) \\
\sin x & \cos x & \sin y \\
-\cos x & \sin x & -\cos y
\end{vmatrix}
...