Question

Prove that the determinant $\begin{vmatrix} x &sin\theta &cos\theta \\\ -sin\theta&-x &1 \\\ cos\theta&1 &x \end{vmatrix}$ is independent of θ.

Answer 1

$\Delta = \begin{vmatrix} x &sin\theta &cos\theta \\\ -sin\theta&-x &1 \\\ cos\theta&1 &x \end{vmatrix}$