If `alpha, beta, gamma` are three distinct real numbers such than `0 < alpha, beta, gamma < pi/2,` then `tan (alpha-beta) + tan (beta-gamma)+tan(gamma-alpha)` is equal to :

If , vecx, vecy are two non-zero and non-collinear vectors satisfying [(a-2)alpha^(2)+ (b-3)alpha+c] vecx + [(a-2)beta^(2)+(b-3)beta+c]vecy + [(a-2)gamma^(2)+(b-3)gamma+c] (vecx xx vecy) = 0, " where " alpha, beta, gamma are three distinct distinct real numbers, then find the value of (a^(2) + b^(2) + c^(2) - 4)

Let alpha, beta, gamma are distinct real numbers. The points with position vectors alpha i + beta j + gamma k , beta i + gamma j + alpha k , gamma i + alpha j + beta k

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 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 ?

Let sin^(-1)alpha+sin^(-1)beta+sin^(-1)gamma=pi and alpha, beta, gamma are non zero real numbers such that (alpha+beta+gamma)(alpha+beta-gamma)=3alphabeta then value of gamma

Let alpha, beta, gamma be distinct real numbers. The points with position vectors alpha hati + beta hatj +gamma hat k , beta hati + gamma hatj +alpha hat k , gamma hati +alpha hatj + beta hatk

Let alpha, beta, gamma be distinct real numbers. The points with position vectors alpha hati + beta hatj +gamma hat k , beta hati + gamma hatj +alpha hat k , gamma hati +alpha hatj + beta hatk