`" if " |{:(sin x,,sin y,,sin z),(cos x,,cos y,,cos z),(cos^(3) x,,cos^(3)y,,cos^(3)z):}|=0` then which of the following is`//`are possible ?

If cot y= (sin x- sin z)/(cos z- cos x) then which of the following is possible?

If cos^(-1)x +cos^(-1)y +cos^(-1)z =3pi then x+y+z is :

If 2(cos(x-y)+cos(y-z)+cos(z-x))=-3 , then :

If sin x+sin y+sin z=3. Find the value of cos x+cos y+cos z

If sin x+ sin y+ sin z=3, then the value of (cos x+ cos y+ cos z) is-

If cos ^(-1) x+cos ^(-1) y+cos ^(-1) z=3 pi then x y+y z+z x=

Statement I The system of linear equations x+(sin alpha )y+(cos alpha )z=0 x+(cos alpha ) y+(sin alpha )z=0 -x+(sin alpha )y-(cos alpha )z=0 has a not trivial solution for only one value of alpha lying between 0 and pi . Statement II |{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0 has no solution in the interval -pi//4 lt x lt pi//4 .

Statement I The system of linear equations x+(sin alpha )y+(cos alpha )z=0 x+(cos alpha ) y+(sin alpha )z=0 -x+(sin alpha )y-(cos alpha )z=0 has a not trivial solution for only one value of alpha lying between 0 and pi . Statement II |{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0 has no solution in the interval -pi//4 lt x lt pi//4 .