If the medians of a triangle ABC makes angles`alpha`,`beta`,`gamma`with each other then show that `cotalpha+cotbeta+cotgamma+cotA+cotB+cotC=0`.

A line makes angles alpha,beta,gammaa n ddelta with the diagonals of a cube. Show that cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4//3.

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

If the median AD of triangle ABC makes an angle pi/4 with the side BC, then find the value of |cotB-cotC|dot

If the line makes angles alpha, beta, gamma, delta with four diagonals of a cube, then the value of cos^(2) alpha+cos^(2) beta+cos^(2) gamma+cos^(2) delta is equal to m/3 . Find m.

If tanbeta=(2sinalphasingamma)/sin(alpha+gamma) , then cotalpha,cotbeta,cotgamma are in

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 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)

The three angular points of a triangle are given by Z=alpha, Z=beta,Z=gamma,w h e r ealpha,beta,gamma are complex numbers, then prove that the perpendicular from the angular point Z=alpha to the opposite side is given by the equation R e((Z-alpha)/(beta-gamma))=0

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If (1+sin alpha)(1+sinbeta)(1+singamma)=(1-sinalpha)(1-sinbeta)(1-singamma) , show that each side is equal to pm cotalpha cotbeta cotgamma .