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,` then for all `theta in (0, (pi)/(2))`

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 ________.

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 ________.

Prove that the determinant |{:(x, sin theta, cos theta),(-sin theta,-x,1),(cos theta,1,x):}| is independent of theta

,x,sin theta,cos theta-sin theta,-x,1cos theta,1,x]|=8, write the value

Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),(cos theta,1,x)| is independent of theta

Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),(cos theta,1,x)| is independent of theta

Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) ]:} is independent of theta.

Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) ]:} is independent of theta.

Prove that the determinant {:|( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) |:} is independent of theta.