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)+tan^(-1)x_3+tan^(-1)x_4=npi+(pi/2)-beta` , where `n` is an integer.

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 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

tan^(-1)2x+tan^(-1)3x=(pi)/(4)

Prove that tan(2tan^(-1)x)=2tan(tan^(-1)x+tan^(-1)x^(3))

tan^(-1)(x/2)+tan^(-1)(x/3)=(pi)/(4)

Prove that tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3)) .

Prove that : tan^(-1).(x)/(x+1)- tan ^(-1) (2x +1) = (3pi)/(4)