If `alpha,beta,gamma, in (0,pi/2)` , then prove that `(sin(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1`

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

If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0

Given alpha+beta-gamma=pi, prove that sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot

If alpha+beta=(pi)/(2) , then prove that cosalpha=sqrt((sinalpha)/(cosbeta)-sinalphacosbeta)

If alpha, beta, gamma are positive acute angles, prove that sin alpha+sin beta+ sin gamma gt sin (alpha+ beta+ gamma)

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma)

If 0 lt alpha lt beta lt gamma lt pi//2 , then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has

The corodinates of the three vertices of a triangle are (a, a tan alpha) , (b ,b tan beta) and (c, c tangamma) . If the circumcentre and orthocentre of the triangle are at (0,0) and (h,k) respectively, prove that (h)/(k)=(cos alpha+ cos beta+ cos gamma)/( sin alpha+ sin beta + sin gamma) .

if alpha , beta , gamma are in A>P show that cot =(sinalpha-singamma)/(cosgammacosalpha)

If sin(alpha+beta)sin(alpha-beta)=singamma(2sinbeta+singamma), where 0 < alpha,beta,gamma < pi, then the straight line whose equation is xsinalpha+ysinbeta-singamma=0 passes through point (a) (1,1) (b) (-1,1) (c) (1,-1) (d) none of these