The determinant $\left|\begin{array}{lll}\sin A & \cos A & \sin A+\cos B \\ \sin B & \cos A & \sin B+\cos B \\ \sin C & \cos A & \sin C+\cos B\end{array}\right|$ is equal to zero.

If the determinant $\left|\begin{array}{lll}x+a & p+u & l+f \\ y+b & q+v & m+g \\ z+c & r+w & n+h\end{array}\right|$ splits into exactly $k$ determinants of order 3, each element of which contains only one term, then the value of $k$ is 8 .

If $\Delta=\left|\begin{array}{lll}a & p & x \\ b & q & y \\ c & r & z\end{array}\right|=16$, then $\Delta_1=\left|\begin{array}{lll}p+x & a+x & a+p \\ q+y & b+y & b+q \\ r+z & c+z & c+r\end{array}\right|=32$.

The maximum value of $\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+\sin \theta & 1 \\ 1 & 1 & 1+\cos \theta\end{array}\right|$ is $\frac{1}{2}$.