`(1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=`

If tan(alpha-beta)=(sin2beta,)/(3-cos2beta) then (a) tanalpha=2tanbeta (b) tanbeta=2tanalpha (c) 2tanalpha=3tanbeta (d) 3tanalpha=2tanbeta

Prove that tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta)

Prove that tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)

Let alpha,betaa n dgamma be some angles in the first quadrant satisfying tan(alpha+beta)=(15)/8a n dcos e cgamma=(17)/8, then which of the following hold(s) good? alpha+beta+gamma=pi cotalpha+tanbeta+tangamma=tanalphatanbetatangamma tanalpha+tanbeta+tangamma=tanalphatanbetatangamma tanalphatanbeta+tanbetatangamma+tangammatanalpha=1

If (tan(alpha+beta-gamma))/("tan"(alpha-beta+gamma))=(tangamma)/(tanbeta),(beta!=gamma) then sin2alpha+sin2beta+sin2gamma= (a) 0 (b) 1 (c) 2 (d) 1/2

Let alpha=som^(-1)((36)/(85)),beta=cos^(-1)(4/5)a n dgamma=tan^(-1)(8/(15)) then cotalpha+cotbeta+cotgamma=cotalphacotbetacotgamma tanalphatanbeta+tanbetatangamma+tanalphatangamma=1 tanalpha+tanbeta+tangamma=tanalphatanbetatangamma cotalphacotbeta+cotbetacotgamma+cotalphacotgamma=1

If tanalpha=1/3,tanbeta=1/7 ,show that 2alpha +beta=pi/4

If tanbeta=(tanalpha+tangamma)/(1+tanalphatangamma)dot prove that sin2beta=(sin2alpha+sin2gamma)/(1+sin2alphasin2gamma) .

Let alpha,beta,gamma>0a n dalpha+beta+gamma=pi/2dot Then prove that sqrt(tanalphatanbeta) + sqrt(t a nbeta"tan"gamma)+sqrt(tanalphatangamma)lt=sqrt(3)

If 3sinbeta=sin(2alpha+beta) then tan(alpha+beta)-2tanalpha is (a)independent of alpha (b)independent of beta (c)dependent of both alpha and beta (d)independent of both alpha and beta