Consider the cubic equation `x^3-x^2+(x-x^2) sin theta +(x-x^2) cos theta +(x-1) sin theta cos theta=0` Whose roots are `alpha, beta, gamma` then

Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin theta + (x -x ^(2)) cos theta + (x-1) sin theta cos theta =0 whose roots are alpha, beta , gamma. The value of ((alpha)/(2))^(2) + ((beta)/(2 )) ^(2) + ((gamma)/(2 ))^(2) =

Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin theta + (x -x ^(2)) cos theta + (x-1) sin theta cos theta =0 whose roots are alpha, beta , gamma. The value of ((alpha)/(2))^(2) + ((beta)/(2 )) ^(2) + ((gamma)/(2 ))^(2) =

Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin theta + (x -x ^(2)) cos theta + (x-1) sin theta cos theta =0 whose roots are alpha, beta , gamma. Number of value of theta in [0,2pi] for which at least two roots are equal, is :

Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin theta + (x -x ^(2)) cos theta + (x-1) sin theta cos theta =0 whose roots are alpha, beta , gamma. Number of value of theta in [0,2pi] for which at least two roots are equal, is :

Consider the cubic equation x^3-(1+cos theta+sin theta)x^2+(cos theta sin theta+cos theta+sin theta)x-sin theta. cos theta =0 Whose roots are x_1, x_2 and x_3

Consider the cubic equation x^3-(1+cos theta+sin theta)x^2+(cos theta sin theta+cos theta+sin theta)x-sin theta. cos theta =0 Whose roots are x_1, x_2 and x_3

Consider the cubic equation x^3-(1+cos theta+sin theta)x^2+(cos theta sin theta+cos theta+sin theta)x-sin theta. cos theta =0 Whose roots are x_1, x_2 and x_3

Consider the cubic equation x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta+cos theta+sin theta)x-sin theta*cos theta=0 Whose roots are x_(1),x_(2) and x_(3)

8sin theta cos theta cos2 theta cos4 theta=sin x rArr x=

cosider the cubic equation : x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta+cos theta+sin theta)x-sin theta cos theta=0 whose roots are x_(1),x_(2),x_(3) .The value of (x_(1))^(2)+(x_(2))^(2)+(x_(3))^(2) equals