Let `x-y sinalpha-z sinbeta= 0 ; x sinalpha-y + z singamma =0` and `x sinbeta + y sin gamma-z=0` be three planes such that `alpha+beta+gamma=pi/2 (alpha, beta, gamma !=0)` then the planes

Let x-y sin alpha-z sin beta=0,x sin alpha=z sin gamma-y=0 and x sin beta+y sin gamma-z=0 be the equations of the planes such that alpha+beta+gamma=pi/2(wherealpha,beta and gamma!=0). Then show there is a common line of intersection of the three given planes.

Let x-ysin alpha-zsin beta=0 , xsin alpha+zsin gamma-y=0 and xsin beta+ysin gamma-z=0 be the equations of the planes such that alpha+beta+gamma=pi//2 (where alpha,beta and gamma!=0)dot Then show that there is a common line of intersection of the three given planes.

Let x-ysin alpha-zsin beta=0 , xsin alpha+zsin gamma-y=0 and xsin beta+ysin gamma-z=0 be the equations of the planes such that alpha+beta+gamma=pi//2 (where alpha,beta and gamma!=0)dot Then show that there is a common line of intersection of the three given planes.

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

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

If alpha + beta+gamma=pi , prove that sin^2 alpha + sin^ beta - sin^2 gamma = 2sinalpha sinbeta cosgamma

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

Statement I The minimum value of the expression sinalpha+sinbeta+singamma where alpha, beta, gamma are real numbers such that alpha+beta+gamma=pi is negative. Statement II If alpha+beta+gamma=pi , then alpha, beta, gamma are the angles of a triangle.

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

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