If ` x = (beta-gamma)(alpha-delta), y = (gamma - alpha)(beta-delta), z= (alpha-beta)(gamma-delta)`, then value of `x^3+y^3+z^3 - 3xyz` is

If x= (beta -gamma )(alpha -delta ), y= (gamma - alpha)(beta -delta ), z=(alpha -beta) (gamma - delta ) then the value of x^(3) +y^(3) +z^(3) -3xyz is : a)0 b) alpha ^(6) +beta ^(6) +gamma ^(6) delta ^(6) c) alpha ^(6) beta^(6) gamma ^(6)delta^(6) d)1

If x=sin(alpha-beta)*sin(gamma-delta), y=sin(beta-gamma)*sin(alpha-delta), z=sin(gamma-alpha)*sin(beta-delta) , then :

If x=sin(alpha-beta)*sin(gamma-delta), y=sin(beta-gamma)*sin(alpha-delta), z=sin(gamma-alpha) *sin(beta-delta) , then :

Assertion A: If x = sin (alpha-beta) sin (gamma-delta), y = sin (beta-gamma) sin (alpha-delta), z = sin (gamma-alpha) * sin (beta-delta) then x + y + z = 0 Reason R: 2sin A sin B = cos (AB) + cos (A + B)

If cos(alpha+beta)sin(gamma+delta)=cos(alpha-beta)sin(gamma-delta) then the value of cot alpha cot beta cot gamma, is

If |((beta+gamma-alpha -delta)^4 , (beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4, (gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4, (alpha + beta-gamma-delta)^2,1)|=-k(alpha -beta)(alpha -gamma)(alpha-delta)(beta-gamma)(beta-delta)(gamma-delta) , then the value of (k)^(1//2) is ____

If cos(alpha+beta)sin(gamma +delta) = cos(alpha-beta)sin(gamma-delta) , then the value of cotalpha*cotbeta.cotgamma is :

Assetion (A) : If x= sin(alpha- beta) sin (gamma- delta), y= sin(beta- gamma) sin (alpha- delta) z=sin (gamma- alpha). Sin (beta- delta) then x+y+z=0 Reason (R) : 2 sin A sin B= cos (A-B)+cos (A+B)

Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4,(gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4,(alpha+beta-gamma-delta)^2,1)|= -64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-delta)(gamma-delta)(gamma-beta)