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

If x+y+z= pi/2 , prove that : cos(x-y-z) + cos(y-z-x) + cos (z-x-y)-4cosx cosy cosz=0

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

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.

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 ?

Find the value of the determinant |"cos"(x-y)"cos"(y-z)"cos"(z-x)"cos"(x+y)"cos"(y+z)cos(z+x)"sin"(x+y)"sin"(y+z)s in(z+x)|

If cosx + cosy + cosz = 0 and sinx + siny + sinz =0 , then show that cos (x-y) + cos(y - z) + cos(z - x) = - 3/2.

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

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

If cos^(-1)x + cos^(-1)y + cos^(-1)z = 3pi, then xy + yz +zx is equal to

If cos^(-1)x + cos^(-1)y + cos^(-1)z = pi, then xy + yz +zx is equal to