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

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

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

If x+y+z=pi/2, then prove that |[sinx,siny,sinz],[cosx,cosy,cosz],[cos^3x,cos^3 y,cos^3z]|=0

If x+y+z=xzy , prove that : x(1-y^2) (1-z^2) + y(1-z^2) (1-x^2) + z (1-x^2) (1-y^2) = 4xyz .

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

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.

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)|

Prove that : |{:(x-y-z ,2x, 2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|=(x+y+z)^(3)

Prove that : cosx+cosy+cosz+cos(x+y+z)=4cos((x+y)/(2))cos((y+z)/(2))cos((z+x)/(2))

If tan x, tan y, tan z are in G.P., show that cos 2y = (cos (x +z))/(cos (x-z)).