Show that `tan^(-1)x > x/(1+(x^2)/3)ifx in (0,oo)dot`

show that tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/sqrt3

If xy =1 +a^(2) , show that tan ^(-1) ""(1)/(a+x) +tan^-1"" 1/(a+y) = tan ^(-1) ""(1)/(a) , ( x+ y + 2a) ne 0

Show that f(x)=1/x is decreasing function on (0,oo)dot

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

Prove that : 1/6tan^(-1)""(2x)/(1-x^2)+1/9tan^(-1)""(3x-x^2)/(1-3x^2)+1/12 tan^(-1)""(4x-4x^3)/((1-6x^2+x^4))= tan^(-1)x

Prove that: tan^(-1)x+tan^(-1)1/x={pi/2,ifx >0-pi/2,ifx<0

Prove that: tan^(-1)x+tan^(-1)1/x={pi/2,ifx >0, -pi/2 if x<0

int_(0)^(oo)((tan^(-1)x)/((1+x^(2))))dx

Show that f(x)={12 x-13 , ifxlt=3 , 2x^2+5 ifx >3 is differentiable at x=3 . Also, find f^(prime)(3)dot

Show that cot^(-1)x={(tan^(-1)(1//x),xgt0),(pi+tan^(-1)(1//x),xlt0):}