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

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