If `alpha,beta "and" gamma` are real number without expanding at any stage prove that
`|{:(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1):}|`=0.

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

alpha,beta and gamma -ray are_____mutagens.

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

If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),cos (gamma-beta),1)] then which of following is/are true ?

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled

Prove that |(sin alpha,cos alpha,sin(alpha+delta)),(sin beta,cos beta,sin(beta+delta)),(sin gamma,cos gamma,sin(gamma+delta))|=0

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

Prove that (cos alpha+cos beta)^(2)+(sin alpha -sin beta)^(2)=4 cos^(2) ((alpha+beta)/(2))

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then