" 1.Prove that the determinant "|[x,sin theta,cos theta],[-sin theta,-x,1],[cos theta,1,x]|" is independent of "theta

Prove that the determinant [x sin theta cos theta-sin theta-x1cos theta1x] is independent of theta.

Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) ]:} is independent of theta.

Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) ]:} is independent of theta.

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

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

,x,sin theta,cos theta-sin theta,-x,1cos theta,1,x]|=8, write the value

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta