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=-2(x^3+x-1)`
B. `Delta_1-Delta_2=-2x^3`
C. `Delta_1+Delta_2=-2x^3`
D. `Delta_1-Delta_2=x(cos 2theta - cos 4 theta)`

Answer

C