If `Delta_(1) =|{:(x, sin theta, cos theta),(-sin theta, -x, 1),(cos theta, 1,x):}|` and `Delta_(2) =|{:(x, sin 2theta, cos 2theta),(-sin 2theta, -x, 1),(cos 2theta, 1,x):}|, x ne 0`, then for all `theta in (0, pi/2)`, Then, `Delta_(1) + Delta_(2) =-2x^(k)`. The value of k is ________.

Options

A. `Delta_(1)-Delta_(2)=-2x^(3)`
B. `Delta_(1)-Delta_(2)=x(cos (2 theta)-cos (4 theta)`
C. `Delta_(1)+Delta_(2)=-2(x^(3)+x-1)`
D. `Delta_(1)+Delta_(2)=-2x^(3)`

Answer

D