If `x_1,x_2, x_3, x_4` are the roots of the equation `x^4-x^3 sin2 beta+ x^2.cos2 beta-xcos beta-sin beta=0`, then `tan^-1x_1+tan^-1x_2+tan^-1x_3+tan^-1x_4` is equal to

If x_(1),x_(2),x_(3),x_(4) are the roots of the equation x^(4)-x^(3)sin2 beta+x^(2)*cos2 beta-x cos beta-sin beta=0, then tan^(-1)x_(1)+tan^(-1)x_(2)+tan^(-1)x_(3)+tan^(-1)x_(4) is equal to

If x_1, x_2, x_3 and x_4 are the roots of the equations x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0, prove that tan^(-1)x_1+tan^(-1)x_2+tan^(-1)x_3+tan^(-1)x_4=(pi/2)-beta .

If x_1, x_2, x_3 and x_4 are the roots of the equations x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0, prove that tan^(-1)x_1+tan^(-1)x_2+tan^(-1)x_3+tan^(-1)x_4=(pi/2)-beta .

If x_1, x_2, x_3,a n dx_4 are the roots of the equations x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0, prove that tan^(-1)x_1+tan^(-1)x_2+tan^(-1)x_3+tan^(-1)x_4=npi+(pi/2)-beta , where n is an integer.

If x_1, x_2, x_3, x_4 are roots of the equation x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0 , then sum_(i=1)^4tan^-1x_i is equal to

If x_(1),x_(2),x_(3),andx_(4) are the roots of the equations x^(4)-x^(3)sin2 beta+x^(2)cos2 beta-x cos beta-sin beta=0, prove that tan^(-1)x_(1)+tan^(-1)x_(2)+tan^(-1)x_(3)+tan^(-1)x_(4)=n pi+((pi)/(2))-beta, where n is an integer.

If tan theta_(1), tan theta_(2) tan theta_(3) and tan theta_(4) are the roots of the equation x^(4) - x^(3) sin 2 beta + x^(2) cos 2 beta - x cos beta - sin beta = "0 then tan" (theta_(1) + theta_(2) + theta_(3) + theta_(4)) is equal to

If tan theta_1,tantheta_2,tan theta_3,tan theta_4 are the roots of the equation x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0 then prove that tan(theta_1+theta_2+theta_3+theta_4)=cot beta