`P(cosalpha,sinalpha), Q(cosbeta, sinbeta) , R(cosgamma, singamma)` are vertices of triangle whose orthocenter is `(0, 0)` then the value of `cos(alpha-beta) + cos(beta-gamma) + cos(gamma-alpha)` is

If ("Cos"alpha, "Sin"alpha,0),(cos beta, sin beta,0), (cos gamma, sin gamma, 0) are vertices of a triangle then circum radius R is

If sinalpha-sinbeta=a and cosalpha+cosbeta=b then write the value of "cos"(alpha+beta) .

If cosalpha+coabeta+cosgamma=0=sinalpha+sinbeta+singamma then cos(alpha+beta)+cos(beta+gamma)+cos(gamma+alpha)=

If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then cos(2alpha-beta-gamma)+cos(2beta-gamma-alpha)+cos(2gamma-alpha-beta)=

If Delta=|(sinalpha,cosalpha,sin(alpha+delta)),(sinbeta,cosbeta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))| then Delta is independent of a) delta only b) alpha, beta, gamma only c) alpha,beta,gamma,delta d)None of these

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

If cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0 , then the value of cos3alpha+cos3beta+cos3gamma is

If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma , then which of the following is/are true:- (a) cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-3/2 (b) cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-1/2 (c) sumcos2alpha+2cos(alpha+beta)+2cos(beta+gamma)+2cos(gamma+alpha)=0 (d) sumsin2alpha+2sin(alpha+beta)+2sin(beta+gamma)+2sin(gamma+alpha)=0