Question

Prove that the determinant `[(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x)]` is independent of `theta`.

Answer 1

Expanding it across R3:- `costheta(sintheta+xcostheta)-1(x+sinthetacostheta)+x(-x^2+(sintheta)^2)` `=>sinthetacostheta+x(costheta)^2+x(sintheta)^2-x-sinthetacostheta-x^3`=`-x^3`