if `xcosalpha+ysinalpha=k=xcosbeta+ysinbeta`,show that `x/(cos((alpha+beta)/2))=y/(sin((alpha+beta)/2))=k/(cos((alpha-beta)/2))`

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

If cos^2alpha-sin^2alpha=tan^2beta ,show that cos^2beta-sin^2beta=tan^2alpha

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

If tanbeta=(nsinalphacosalpha)/(1-nsin^2alpha) ,show that tan(alpha-beta)=(1-n)tanalpha

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

If asin(theta+alpha)=b sin (theta+beta) ,show that tantheta=(bsinbeta-asinalpha)/(acosalpha-bcosbeta)

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

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