Prove that: `tan^-1(t) +tan^-1 ((2t)/(1-t^2))=tan^-1( (3t-t^3)/(1-3t^2)), if - 1/sqrt(3),tlt 1/sqrt(3)`

Prove that tan^(-1)x+tan^(-1)(2x)/(1-x^2)=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/(sqrt(3))

If x=sin^(-1)((2t)/(1+t^2)) and y= tan^(-1)((2t)/(1-t^2)),t > 1 . Prove that dy/dx=-1

Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , |x|<1/sqrt3 w.r.t tan^(-1)(x/sqrt(1-x^2))

If x=sin^(-1)[(2t)/(1+t^2)]'and'y=tan^(-1)((2t)/(1-t^2)), prove that dy/dx=1'.

If x=sin^(-1)((2t)/(1+t^2))a n d \ y=tan^(-1)((2t)/(1-t^2)),t > 1. P rov e \ t h a t(dy)/(dx)=-1

The value of (3-tan^2A)/(1-3tan^2A)+(3-tan^2B)/(1-3tan^2A)+(3-tan^2C)/(1-3tan^2\ \ C) is a. 1 b. \ 0 c. \ 1+sqrt(3) d. 1-sqrt(3)

Prove that : t a n A+tan(60^0+A)+tan(120^0+A)=3t a n3A

Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

Prove that: tan4theta=(4t a ntheta(1-tan^2theta))/(1-6tan^2theta+tan^4theta)