`|{:(1,cos alpha, cos beta),(cos alpha, 1,cosgamma),(cosbeta,cosgamma,1):}|=|{:(0,cosalpha,cosbeta),(cosalpha,0,cosbeta),(cosbeta,cosgamma,0):}|`
if `cos^(2)alpha+cos^(2)beta+cos^(2)gamma=`

|(1,cosalpha,cosbeta),(cosalpha,1,cosgamma),(cosbeta,cosgamma,1)|=|(0,cosalpha,cosbeta),(cosalpha,0,cosgamma),(cosbeta,cosgamma,0)|" if " cos^(2)alpha+cos^(2)beta+cos^(2)gamma= a)1 b)2 c) 3//2 d) 1//2

IF Delta_1=|{:(1,cosalpha,cosbeta),(cosalpha,1,coygamma),(cosbeta,cosgamma,1):}|,Delta_2|{:(0,cosalpha,cosbeta),(cosalpha,0,cosgamma),(cosbeta,cosgamma,0):}| and Delta_1=Delta_2 then show that cos^2alpha+cos^2beta+cos^2gamma=1

|{:(0," "sinalpha,-cosbeta),(cosalpha," "0," "sinbeta),(cos alpha,-sinbeta," "0):}|

If cosalpha+cosbeta+cosgamma=0=sin alpha+sinbeta+singamma then cos^2alpha+cos^2beta+cos^2gamma=

If secalpha+secbeta+secgamma=0 ,show that (cosalpha+cosbeta+cosgamma)^2=cos^2alpha+cos^2beta+cos^2gamma

|{:(cosalpha cos beta,cos alpha sin beta ,-sin alpha),(-sin beta,cos beta," "0),(sin alpha cosbeta ,sinalpha sin beta ,""cos alpha):}|

If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+cos3gamma=12cosalphacosbetacosgamma

If alpha,beta and gamma are such that alpha+beta+gamma=0, then |(1,cos gamma,cosbeta),(cosgamma,1,cos alpha),(cosbeta,cos alpha,1)|

Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos(alpha+beta)/(2)cos(beta+gamma)/2cos(gamma+alpha)/2

If alpha,beta and gamma are such that alpha+beta+gamma=0 , then |(1,cos gamma,cosbeta),(cosgamma,1,cos alpha),(cosbeta,cos alpha,1)|