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

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

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

If cos^2theta- sin^2theta= tan^2 phi , then prove that cos^2phi – sin^2phi= tan^2theta

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

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

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

If tan^2theta=1+2tan^2phi ,show that cos2phi=1+2cos2theta

Find cot^2 theta - sin^2 alpha . .

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

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