If `("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c` `(a+b)/(a-b)s in^2(alpha-beta)+(b+c)/(b-c)s in^2(beta-gamma)+(c+a)/(c-a)s in^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

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 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 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)(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 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

Prove that: tan(alpha-beta)+tan(beta-gamma)+tan (gamma-alpha) = tan(alpha-beta) tan (beta-gamma) tan (gamma-alpha) .

If (tan(alpha+beta-gamma))/(tan(alpha-beta+gamma))=(tan gamma)/(tan beta),(beta!=gamma) then sin2 alpha+sin2 beta+sin2 gamma=(a)0(b)1(c)2(d)(1)/(2)

If a=cisalpha,b=cisbeta,c=cisgamma , and a/b+b/c+c/a-1=0 then cos(alpha-beta)+cos(beta-gamma) + cos(gamma-alpha) =