`tan^(- 1) (1/(x+y)) +tan^(- 1) (y/(x^2+x y+1)) =cot^(- 1)x`

Prove that : tan^(-1)((x-y)/(1+xy)) + tan^(-1)((y-z)/(1+yz)) + tan^(-1)( (z-x)/(1+zx)) = tan^(-1)((x^2-y^2)/(1+x^2y^2))+tan^(-1)((y^2-z^2)/(1+y^2z^2))+tan^(-1)((z^2-x^2)/(1+z^2x^2))

Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt((1+x^2) (1+y^2))))

Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt((1+x^2)(1+y^2))))

Prove that : tan^(-1) x+cot^(-1) y = tan^(-1) ((xy+1)/(y-x))

Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x

If tan^(-1) x + tan^(-1) y = (4pi)/(5) , then cot^(-1) x + cot^(-1) y equal to

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

The solution of the differential equation (dy)/(dx)=(x^2+x y+y^2)/(x^2), is a.) tan^(-1)(x/y)=logy+C b.) tan^(-1)(y/x)=logx+C c.) tan^(-1)(x/y)=logx+C d.) tan^(-1)(y/x)=logy+C

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

2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to (2x)/(1-x^2) t(2tan^(-1)x) tan(cot^(-1)(-x)-cot^(-1)(x)) "tan"(2cot^(-1)x)