`(alpha)/(beta)`+`(beta)/(alpha)`

|(alpha,-beta,0),(0,alpha,beta),(beta,0,alpha)|=0 , then

(without alpha + without beta-sin (alpha + beta)) / (without alpha + without beta + sin (alpha + beta)) = tan ((alpha) / (2)) tan ((beta) / (2))

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

Prove that : |[alpha+beta+gamma,-gamma,-beta],[-gamma, alpha+beta+gamma, -alpha],[-beta,-alpha,alpha+beta+gamma]|= 2(alpha+beta)(beta+gamma)(gamma+alpha)

(tan alpha + tan beta )/( tan (alpha + beta ))+(tan alpha - tan beta )/(tan (alpha - beta )) =

If alpha,beta are the zeroes of f(x)=2x^2+6x-6 ,then a) alpha+beta+alpha beta=0 b) alpha+beta=alpha beta c) alpha+betagtalpha beta d) alpha+betaltalpha beta

The expression (tan alpha+tan beta)cot(alpha+beta)+(tan alpha-tan beta)cot(alpha-beta) is independent of both alpha and beta.

Prove that, |{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta):}|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)

Prove that: |[alpha,beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,gamma+alpha,alpha+beta]|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma) .