If $\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=$ $Ax ^{3}+ Bx ^{2}+ Cx + D ,$ then $B + C$ is equal to

$$f(x)=\left| {\begin{array}{*{20}{c}} {{{\sin }^2}x}&{ – 2 + {{\cos }^2}x}&{\cos 2x} \\ {2 + {{\sin }^2}x}&{{{\cos }^2}x}&{\cos 2x} \\ {{{\sin }^2}x}&{{{\cos }^2}x}&{1 + \cos 2x} \end{array}} \right| ,x \in[0, \pi]$$

Then the maximum value of $f(x)$ is equal to $…..$

The parameter on which the value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&a&{{a^2}}\\{\cos (p – d)x}&{\cos px}&{\cos (p + d)x}\\{\sin (p – d)x}&{\sin px}&{\sin (p + d)x}\end{array}\,} \right|$ does not depend upon

If $a, b, c$  are all different and $\left| {\,\begin{array}{*{20}{c}}a&{{a^3}}&{{a^4} – 1}\\b&{{b^3}}&{{b^4} – 1}\\c&{{c^3}}&{{c^4} – 1}\end{array}\,} \right|$ = $0$ , then the value of $abc(ab + bc + ca)$ is