If `f(x)=|(cos(x+alpha),cos(x+beta),cos(x+gamma)),(sin(x+alpha),sin(x+beta),sin(x+gamma)),(sin(beta-gamma),sin(gamma-alpha),sin(alpha-beta))|` and f(2)=6, then find `1/5 sum_(r=1)^25 f(r)`,

" If " f(x) = |{:(cos(x+alpha),,cos(x+beta),,cos(x+gamma)),(sin(x+alpha) ,,sin(x+beta),,sin(x+gamma)),(sin(beta-gamma),, sin(gamma-alpha),,sin (alpha-beta)):}| and f(0)=2 theb find the value of Sigma_(r=1)^(30) | f(r )| .

If f(x) = |{:(cos (x+alpha),cos(x+beta),cos(x+gamma)),(sin (x+alpha),sin(x+beta),sin(x+gamma)),(sin(beta+gamma),sin(gamma+alpha),sin(alpha+beta)):}| then f(theta)-2f(phi)+f(psi) is equal to

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

If cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma , then (sin3alpha+sin3beta+sin3gamma)/(sin(alpha+beta+gamma)) is equal to

If x=sin(alpha-beta)*sin(gamma-delta), y=sin(beta-gamma)*sin(alpha-delta), z=sin(gamma-alpha) *sin(beta-delta) , then :

Let A and B denote the statements A : cos alpha + cos beta + cos gamma =0 B : sin alpha + siin beta + sin gamma = 0 If cos(beta - gamma) + cos (gamma -alpha) + cos (alpha -beta) = - (3)/(2) , then

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and gamma are in

If a=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin gamma and b/c+c/a+a/b=1, then cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=

Prove that: |(sinalpha, cosalpha, 1),(sinbeta, cosbeta, 1),(singamma, cosgamma, 1)|=sin(alpha-beta)+sin(beta-gamma)+sin(gamma-alpha)

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