[" 82.If "sin(alpha+beta)sin(alpha-beta)=sin gamma(2sin beta+sin gamma)," where "],[0

If "sin"(alpha + beta) "sin" (alpha-beta) = "sin" gamma(2"sin" beta + "sin"gamma) " where " 0 lt alpha, beta, lt pi, then the straight line whose equation is x "sin" alpha+y "sin" beta-"sin" gamma = 0 passes through the point

|(0, sin alpha, sin beta),(sin alpha, 0, sin gamma),(sin beta, sin gamma, 0)|=|(1, sin alpha, sin beta),(sin alpha, 1, sin gamma),(sin beta, sin gamma, 1)| , then

Let alpha,beta and gamma are the angles of a right angle triangle,then the value of sin alpha*sin beta*sin(alpha-beta)+sin beta*sin gamma*sin(beta-gamma)+sin gamma*sin alpha*sin(gamma-beta)+sin(beta-gamma)*sin(gamma-gamma)*sin(gamma-

The value of the determinant Delta = |(sin 2 alpha,sin (alpha + beta),sin (alpha + gamma)),(sin (beta + gamma),sin 2 beta,sin (gamma + beta)),((sin gamma + alpha),sin (gamma + beta),sin 2 gamma)| , is

The value of the determinant Delta = |(sin 2 alpha,sin (alpha + beta),sin (alpha + gamma)),(sin (beta + gamma),sin 2 beta,sin (gamma + beta)),((sin gamma + alpha),sin (gamma + beta),sin 2 gamma)| , is

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)=

If (tan (alpha- beta+ gamma))/(tan (alpha+ beta- gamma))=(tan beta)/( tan gamma) , show that either sin (beta- gamma)=0 or sin 2 alpha+ sin 2 beta+ sin 2 gamma=0

Let x-y sin alpha-z sin beta=0;x sin alpha-y+z sin gamma=0 and x sin beta+y sin gamma-z=0 be three planes such that alpha+beta+gamma=(pi)/(2)(alpha,beta,gamma!=0) then the planes

If sin alpha+ sin beta+ sin gamma=3, then sin^3alpha+sin^3beta+sin^3 gamma=