[" 4."cos alpha*sin(beta-gamma)+cos beta*sin(gamma-alpha)],[+cos gamma*sin(alpha-beta)=]

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

If origin is the orthocentre of the triangle with vertices A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then cos(2 alpha-beta-gamma)+cos(2 beta-gamma-alpha)+cos(2 gamma-alpha-beta)=

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

If alpha,beta,gamma do not differ by a multiple of pi and if (cos(alpha+theta))/(sin(beta+gamma))=(cos(beta+theta))/(sin(gamma+alpha))=(cos(gamma+theta))/(sin(alpha+beta))=k Then k equals to

If cos (beta - gamma) + cos (gamma - alpha) + cos (alpha - beta) = -3/2, "show that", cos alpha + cos beta + cos gamma = 0 "and" sin alpha + sin beta + singamma = 0."Hence deduce that," cos (beta - gamma) = cos (gamma - alpha) = cos (alpha - beta) = -1/2.

If cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma then x^(sin(2 alpha-beta-gamma)*x^(sin(2 beta-gamma-alpha)))*x ^(sin(2 gamma-alpha-beta)) is

If Delta = det [[sin alpha, cos alpha, sin alpha + cos alphasin beta, cos alpha, sin beta + cos betasin gamma, cos alpha, sin gamma + cos beta]] then Delta