If `x/("tan"(theta+alpha))=y/("tan"(theta+beta))=z/(tan(theta+gamma)),` then show that `sum(x+y)/(x-y)sin^2(alpha-beta)=0`

If x/(tan(theta+alpha)) = y/(tan(theta+beta)) =z/(tan(theta+gamma)) , show that sum (x+y)/(x-y) sin^(2)(alpha-beta) =0

If (x)/(tan (theta+ alpha))=(y)/(tan (theta+ beta))=(z)/(tan (theta+ gamma) then sum (x+y)/(x-y) sin^(2)(alpha- beta)=

If x/(tan (theta + alpha)) = y/(tan (theta + beta)) = z/tan(theta + gamma), "prove that" (x+y)/(x-y)sin^(2) (alpha - beta) + (y + z)/(y - z) sin^(2) (beta - gamma) + (z + x)/(z-x) sin^(2) (gamma - alpha ) = 0

If (x)/(tan( theta + alpha ))=(y)/(tan (theta + beta ))=(z)/(tan ( theta + gamma)) , then sum(x+y)/(x-y) sin^(2)(alpha - beta )=

If (x)/(tan(theta-alpha)) = (y)/(tan(theta+beta)) = (z)/(tan(theta+gamma)) then sum(x+y)/(x-y)sin^(2)(alpha-beta) is equal to :

If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c then prove (a+b)/(a-b)sin^2(alpha-beta)+(b+c)/(b-c)sin^2(beta-gamma)+(c+a)/(c-a)sin^2(gamma-alpha)=0

If (tan (theta+alpha))/a= (tan (theta+beta))/b= (tan (theta+ gamma))/c , prove that : (a+b)/(a-b) sin^2 (alpha- beta) +(b+c)/(b-c) sin^2 (beta-gamma)+ (c+a)/(c-a) sin^2 (gamma-alpha)=0 .

If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c then prove (a+b)/(a-b)sin^2(alpha-beta)+(b+c)/(b-c)sin^2(beta-gamma)+(c+a)/(c-a)sin^2(gamma-alpha)=0

If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c then (a+b)/(a-b)sin^2(alpha-beta)+(b+c)/(b-c)sin^2(beta-gamma)+(c+a)/(c-a)sin^2(gamma-alpha)=0

If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c (a+b)/(a-b)sin^2(alpha-beta)+(b+c)/(b-c)sin^2(beta-gamma)+(c+a)/(c-a)sin^2(gamma-alpha)=0