If `alpha+beta+gamma=0`,prove that `cosalpha+cosbeta+cosgamma=4cos(alpha/2)cos(beta/2)cos(gamma/2)-1`

If alpha+beta=gamma ,show that cos^2alpha+cos^2beta+cos^2gamma=1+2cosalphacosbetacosgamma

If secalpha+secbeta+secgamma=0 ,show that (cosalpha+cosbeta+cosgamma)^2=cos^2alpha+cos^2beta+cos^2gamma

Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4 cos((alpha+beta)/2)cos((beta+gamma)/2)cos((gamma+alpha)/2)

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

If tan^2alpha = 1 + tan^2beta ,then prove that cos^2 beta = cot^2alpha

Prove that (cos alpha-cos beta)^2+(sin alpha-sin beta)^2=4sin^2((alpha-beta)/2)

Prove that cos 4A=1-8cos^2A+8 cos^4A

if tanalpha , tanbeta are the roots of x^2+px+q=0 ,show that sin^2(alpha+beta)+p sin(alpha+beta)cos(alpha+beta)+q cos^2(alpha+beta)=q

If tan alpha=m/(m+1) and tan beta=1/(2m+1) ,prove that alpha+beta=pi/4 .