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`

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

if alpha+beta+gamma=2pi prove that cos^2alpha+cos^2beta+cos^2gamma-2cosalphacosbetacosgamma=1

If sin alpha + sin beta + sin gamma =3, then the value of (cos alpha + cos beta+ cos gamma) is-

Given alpha+beta-gamma=pi, prove that sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma)

If alpha,beta,gamma, in (0,pi/2) , then prove that (sin(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If cos alpha+ cos beta+ cos gamma + cos alpha cos beta cos gamma=0 , show that sin alpha (1+ cos beta cos gamma)=+- sin beta sin gamma .

If cos beta cos (gamma- alpha)= cos (alpha- beta+ gamma) , prove that cot alpha+ cot y= 2cot beta

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

If cos (beta - gamma) + cos (gamma - alpha) + cos (alpha - beta) = -3/2, "show that", cos alpha + cos beta + cos gamma = 0 "and" sin alpha + sin beta + singamma = 0."Hence deduce that," cos (beta - gamma) = cos (gamma - alpha) = cos (alpha - beta) = -1/2.