If `cos(y-z)+cos(z-x)+cos(x-y)=-3/2,` prove that `cos x + cos y + cos z = 0 = sin x + siny + sinz.`

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

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

Given that cos(x-y) +cos (y-z) +cos (z-x)=-3/5 find cos x+ cos y + cos z

lf cos x + cosy-cos z = 0 = sin x + sin y + sin z then cos((x-y)/2)=

Prove that : (cos x + cos y)^2 + (sin x - sin y)^2 = 4 cos^2\ (x+y)/2

Let x,y,z in (0, (pi)/(2)) are first three consecutive terms of an arithmatic progression such that cos x + cos y + cos z =1 and sin x + sin y + sin z = (1)/(sqrt2), then which of the following is/are correct ?

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi , prove that x^2+y^2+z^2+2x y z=1.

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi , prove that x^2+y^2+z^2+2x y z=1.

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 .

Prove that : (sin x - sin y)/(cos x + cos y) = tan ((x-y)/2)