`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

P(cos alpha,sin alpha),Q(cos beta,sin beta),R(cos gamma,sin gamma) are vertices of triangle whose orthocenter is (0,0) then the value of cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha) is

Let A = (cos alpha, sin alpha), B = (cos beta , sin beta), C = (cos gamma, sin gamma) . If origin is the orthocentre of the Delta ABC , then the value of sum cos (2 alpha - beta - gamma)= ____________

Delta ABC has vertices A(a cos alpha,a sin alpha),B(a cos beta,a sin beta) and C(a cos gamma,a sin gamma) then its orthocentre is

If cosalpha, cosbeta and cosgamma are the direction cosine of a line, then find the value of cos^2alpha+(cosbeta+singamma)(cosbeta-singamma) .

If A=(cos alpha,sin alpha,0), B=(cos beta,sin beta,0),C=(cos gamma,sin gamma,0) are vertices of Delta ABC and cos alpha+cos beta+cos gamma=3a, sin alpha+sin beta+sin gamma=3b then orthocentre is

Prove that : cos^2 (beta-gamma) + cos^2 (gamma-alpha) + cos^2 (alpha-beta) =1+2cos (beta-gamma) cos (gamma-alpha) cos (alpha-beta) .

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is :

cos (alpha + beta) cos gamma-cos (beta + gamma) cos alpha = sin beta sin (gamma-alpha)

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta) =