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 :`2sinAsinB=cos(A-B)+cos(A+B)`

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)

If x = sin (alpha - beta) sin (gamma - delta) y = sin (beta - gamma) sin (alpha - delta ) and z = sin (gamma - alpha ) sin (beta - delta ) then

If cos (alpha + beta) sin (gamma + delta) = cos (alpha - beta) sin (gamma - delta) then:

cos (alpha + beta) cos gamma-cos (beta + gamma) cos alpha = sin beta sin (gamma-alpha)

sin(beta+gamma-alpha)+sin(gamma+alpha-beta)+sin(alpha+beta-gamma)-sin(alpha+beta+gamma)=

sin (beta+ gamma- alpha) + sin (gamma+ alpha - beta) + sin (alpha + beta- gamma)- sin (alpha + beta + gamma)=

sin (beta+ gamma- alpha) + sin (gamma+ alpha - beta) + sin (alpha + beta- gamma)- sin (alpha + beta + gamma)=

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta) =

cos alpha sin (beta-gamma)+cos beta sin (gamma-alpha) +cos gamma(sin alpha-beta)=