If `cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2` , prove that `cosalpha+cosbeta+cosgamma=s inalpha+s inbeta+s ingamma=0`

If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled

If 2(cos ( alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)+3=0 , prove that (d alpha)/(sin ( beta+theta)sin(gamma+theta))+(d beta)/(sin(alpha+beta)sin(beta+theta))+(d gamma)/(sin(alpha+theta)sin(beta+theta))=0 , where, 'theta' is any real angle such that alpha+theta, beta+theta, gamma+theta are not the multiple of pi .

If cos(alpha+beta)*sin(gamma+delta)=cos(alpha-beta)*sin(gamma-delta), prove that cotalphacotbetacotgamma=cotdelta

If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+cos3gamma=12cosalphacosbetacosgamma

The expression cos^(2)(alpha + beta + gamma) + cos^(2)(beta + gamma) + cos^(2)alpha - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma) is (a) independent of alpha (b) independent of beta (c) dependent on gamma only (d) dependent on alpha, beta, gamma

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma , then which of the following is/are true:- (a) cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-3/2 (b) cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-1/2 (c) sumcos2alpha+2cos(alpha+beta)+2cos(beta+gamma)+2cos(gamma+alpha)=0 (d) sumsin2alpha+2sin(alpha+beta)+2sin(beta+gamma)+2sin(gamma+alpha)=0

If cos(alpha+beta)sin(gamma+delta)="cos"(alpha-beta)"sin"(gamma-delta) , prove that cotalphacotbetacotgamma=cotdelta

If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)