Inverse Trignometry: if x1,x2,x3,x4 are roots of eqn, then find sum of tan^-1 x

[namitha]

If x1,x2,x3,x4 are the roots of the equation x⁴-x³


sin2(Beta)+x² cos 2(Beta)-x cos(Beta)-sin(Beta)=0 then
summation i=1 to 4 of tan^-1 x_i is ?

 

[Deleted member 4993]

If x1,x2,x3,x4 are the roots of the equation x⁴-x³


sin2(Beta)+x² cos 2(Beta)-x cos(Beta)-sin(Beta)=0 then
summation i=1 to 4 of tan^-1 x_i is ?

What are the real roots of:

x⁴-= x * (x³ - 1) = x * (x - 1)(x² + x + 1)

Continue....

 

[stapel]

...the equation x⁴-x³


sin2(Beta)+x² cos 2(Beta)-x cos(Beta)-sin(Beta)=0...

Are the two lines above actually supposed to be one? In particular, is "the equation" supposed to be as follows?

. . . . .x⁴ - x³ sin2(Beta) + x² cos 2(Beta) - x cos(Beta) - sin(Beta) = 0

When you reply, please include a clear listing of your thoughts and efforts so far, so we can see where you're needing assistance. Thank you!