If `alphagt0, betagt0, gammagt0` and `alpha+beta+gamma lt pi/2` show that `tanalphatanbeta+tanbetatangamma+tangammatanalphalt1`

If alphagt0, betagt0, gammagt0, alpha+beta+gamma= pi show that sin^2alpha+sin^2beta-sin^2gamma =

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)

Let alpha,beta,gamma > 0 and alpha+beta+gamma=pi/2. Statement-1: |tan alpha tan beta-(a!)/6|+|tan beta tan gamma-(b!)/2|+|tan gamma tanalpha-(c!)/3| le 0, where n! =1.2..........n, then tan alpha tanbeta,tanbeta tangamma, tan gamma tan alpha=1 Settlement 2 : tan alpha tanbeta+,tanbeta tangamma+, tan gamma tan alpha=1

If 0ltalphaltbetaltpi/2, show that (sinalpha)/alphagt(sinbeta)/beta

If 0 lt alpha lt beta lt (pi)/(2) then

If 0 lt alpha lt pi/2 then show that tanalpha+cotalphagtsinalpha+cosalpha

(a) show that alpha^2 + beta^2 + alpha beta =0

If alpha + beta + gamma = pi , show that : tan (beta+gamma-alpha) + tan (gamma+alpha-beta) + tan (alpha+beta-gamma) = tan (beta+gamma-alpha) tan (gamma+alpha-beta) tan (alpha+beta-gamma)

If alpha+beta+gamma=2pi , then show that tan.alpha/2 + tan.beta/2 + tan.gamma/2 = tan.alpha/2 tan.beta/2 tan.gamma/2 .

If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,beta,gamma],[beta,gamma,alpha],[gamma,alpha,beta]|=0, alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha , and gamma+alpha-beta .