If the distances of the vertices of a triangle =ABC from the points of contacts of the incercle with sides are `alpha,betaa n dgamma` then prove that `r^2=(alphabetagamma)/(alpha+beta+gamma)`

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 alpha+beta+gamma=2pi prove that cos^2alpha+cos^2beta+cos^2gamma-2cosalphacosbetacosgamma=1

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

If the distance of the point (alpha,2) from its chord of contact w.r.t. the parabola y^2=4x is 4, then find the value of alphadot

If alpha,betaa n dgamma are the roots of x^3+8=0 then find the equation whose roots are alpha^2,beta^2a n dgamma^2 .

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

A tower P Q stands at a point P within the triangular park A B C such that the sides a , ba n dc of the triangle subtend equal angles at P , the foot of the tower. if the tower subtends angles alpha,betaa n dgamma,a tA , Ba n dC respectively, then prove that a^2(cotbeta-cotgamma)+b^2(cotgamma-cotalpha)+a^2(cotalpha-cotbeta)=0

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

A line makes angles alpha,betaa n dgamma with the coordinate axes. If alpha+beta=90^0, then find gammadot