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

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

If tanalpha=(asinbeta)/(1-acosbeta) and tanbeta=(bsinalpha)/(1-bcosalpha) ,prove that bsinalpha=asinbeta

If alpha and beta be two acute angles and cos2alpha=(3cos2beta-1)/(3-cos2beta) ,show that tan alpha=sqrt2tanbeta

If 2 tan beta + cot beta = tan alpha , prove that 2 tan (alpha-beta) = cot beta

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

Find cot^2 alpha- cos^2 alpha . .

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 sin(theta+alpha)=nsin(theta-alpha) and n!=-1 ,prove that cottheta=(n-1)/(n+1)cotalpha

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