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

Prove that the determinate abs([x,sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]) is independent of theta

Prove that |[x, sintheta, costheta],[-sintheta, -x, 1],[costheta, 1, x]| is independent of theta

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

If sintheta+costheta=x then sintheta-costheta=?

Evaluate the determinates abs([-costheta,-sin theta],[sintheta,-costheta])

Evaluate the determinants in |{:(costheta,-sintheta),(sintheta,costheta):}|

If sintheta-costheta=1 ,then find sintheta.costheta

If sintheta+costheta=1 , then Find sintheta.costheta

If |{:(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x):}|=8 , then the value of x is :