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). Then prove that sqrt(tan alpha tan beta)+sqrt(tan beta tan gamma)+sqrt(tan alpha tan gamma)<=sqrt(3)

If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then prove that tan alpha=tan beta+2 tan gamma .

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 tan alpha-(c!)/(3)|<=0 where n!=1.2............n, then tan alpha tan beta,tan beta tan gamma,tan gamma tan alpha=1

if 0ltalpha,beta,gamma lt(pi/2) prove that sin alpha+sin beta+sin gamma gtsin(alpha+beta+gamma)

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

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 alpha,beta,gamma,in(0,(pi)/(2)), then prove that (si(alpha+beta+gamma))/(sin alpha+sin beta+sin gamma)<1

If (tan (alpha- beta+ gamma))/(tan (alpha+ beta- gamma))=(tan beta)/( tan gamma) , show that either sin (beta- gamma)=0 or sin 2 alpha+ sin 2 beta+ sin 2 gamma=0

If (tan(alpha + beta - gamma))/(tan(alpha - beta + gamma)) = (tan gamma)/(tan beta), (beta ne gamma) , then sin 2alpha + sin 2beta + sin 2gamma=

If tan beta=(tan alpha + tan gamma)/(1+ tan alpha . tan gamma) Prove that sin 2 beta =(sin 2 alpha + sin 2 gamma)/(1+ sin 2 alpha . Sin 2 gamma)