If `t a nalpha,t a nbeta,t a ngamma` are the roots of the equation `x^3-p x^2-r=0,` then the value of `(1+tan^2alpha)(1+tan^2beta)(1+tan^2gamma)` is equal to `(p-r)^2` b. `1+(p-r)^2` c. `1+(p-r)^2` d. none of these

If tan alpha, tan beta, tan gamma are the roots of the equation x^(3)-px^(2)-r=0, then the value of (1+tan^(2)alpha)(1+tan^(2)beta)quad (1+tan^(2)gamma) is equal to (p-r)^(2) b.1+(p-r)^(2) c.1+(p-r)^(2) d.none of these

If tan alpha, tan beta, tan lambda are the roots of the equation x^(3) - px^(2) - r = 0 then the value of (1+tan^(2) alpha) (1+tan^(2) beta)(1+tan^(2)lambda) =

If alpha , beta gamma are the roots of the equation x^3+px^2+qx+r=0 , then (1-alpha^2)(1-beta^2)(1-gamma^2) is equal to (a) (1+q)^2-(p+r)^2 (b) (1+q)^2+(p+r)^2 (c) (1-q)^2+(p-r)^2 (d) none of these

If r,s,t are the roots of the equation x(x-2)(3x-7)=2 ,then the value of tan^(-1)(r)+tan^(-1)(s)+tan^(-1)(t) is

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

If alpha,beta,gamma are the roots of the equation,x^(3)+P_(0)x^(2)+P_(1)x+P_(2)=0 ,then (1-alpha^(2))(1-beta^(2))(1-gamma^(2)) is equal to

If alpha, beta, gamma are roots of the equation x^(3)+px^(2)+qx+r= 0 , then prove that (1-alpha^(2))(1- beta^(2)) (1- gamma^(2))=(1+q)^(2)-(p+r)^(2)

If alpha,beta, gamma re the roots of the equations x^3+px^2+2x+p=0 then the general value of tan^-1 alpha+tan^-1 beta+tan^-1 gamma is (A) npi (B) (npi)/2 (C) (2n+1) pi/2 (D) dependent upon the value of p.