If `alpha + beta + gamma=pi, ` then the value of `sin ^(2) alpha + sin ^(2) beta - sin^(2) gamma `is equal to

If alpha + beta - gamma =pi, then sin ^(2) alpha + sin^(2) beta- sin ^(2) gamma=

If sin alpha+sin beta+sin gamma=0=cos alpha+cos beta+cos gamma, then the value of sin^(2)alpha+sin^(2)beta+sin^(2)gamma, is

If alpha, beta, gamma are acute angles and cos theta = sin beta//sin alpha, cos phi = sin gamma//sin alpha and cos(theta-phi)=sin beta sin gamma then the value of of tan^(2)alpha - tan^(2)beta- tan^(2)gamma is equal to

If alpha + beta- gamma= pi , prove that sin^(2)alpha + sin^(2)beta - sin^(2)gamma = 2sin alpha sin beta cos gamma .

If alpha, beta , gamma are angles of a triangle then the value of (sin^(2) alpha + sin ^(2) beta+sin ^(2) gamma-2 cos alpha cos beta cos gamma) is-

If alpha+beta-gamma=pi , then sin^(2)alpha=sin^(2)beta-sin^(2)gamma is equal to

If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then (a) sin ^ (2) alpha + sin ^ (2) beta + sin ^ (2) gamma = (3) / ( 2) (b) sin ^ (2) alpha + sin ^ (2) beta + sin ^ (2) gamma = (3) / (4) (c) cos ^ (alpha) + cos ^ (2) beta + cos ^ (2) gamma = (3) / (2) (d) cos ^ (2) alpha + cos2 beta + cos2 gamma = -1