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

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

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

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

(sintheta-costheta+1)/(sintheta+costheta-1) is equal to

Let triangle1=|{:(x,sintheta,costheta),(-sintheta,x,1),(costheta,1,x):}| and triangle2=|{:(x,sin2theta,cos2theta),(-sin2theta,x,1),(cos2theta,1,x):}| then which of following is/are true?