For all values of $A,B,C$ and $P,Q,R$ the value of the determinant $(x+a)^3\small\begin{vmatrix}\cos(A-P)&\cos (A-Q)&\cos(A-R)\\\cos(B-P)&\cos(B-Q)&\cos(B-R)\\\cos(C-P)&\cos(C-Q)&\cos(C-R)\end{vmatrix}$ is

Question

$(a)\;1\qquad(b)\;0\qquad(c)\;2\qquad(d)\;None\;of\;these$