Prove that: `"tan"^(-1)(m)/(n)-tan^(-1)((m-n)/(m+n))=(pi)/(4). m, n gt 0`

Prove that: tan^(-1)((m)/(n))+tan^(-1)((n-m)/(n+m))=[(pi)/(4)(m)/(n)>;-1(-3 pi)/(4)(m)/(n)<-1

What is the value of tan^(-1)((m)/(n))-tan^(-1)((m-n)/(m+n)) ?

What is the value of tan^(-1)((m)/(n))-tan^(-1)((m-n)/(m+n))?

Statement 1: If agt0,bgt0, tan^(-1)(a/x)+tan^(-1)(b/x)=(pi)/2 . implies x=sqrt(ab) Statement 2: If m,n epsilonN,ngem, then "tan"^(-1)(m/n)+tan^(-1)(n-m)/(n+m)=(pi)/4 .

Prove that: sum_(m=1)^(n)tan^(-1)((2m)/(m^(4)+m^(2)+2))=tan^(-1)((n^(2)+n)/(n^(2)+n+2))

(tan^(-1)((1)/(3))+tan^(-1)((1)/(7))+tan^(-1)((1)/(13))+......+tan^(-1)((1)/(381)))=(m)/(n) where m,n in N, then find least value of (m+n)

If the sum sum_(n=1)^(10)sum_(m=1)^(10)tan^(-1)((m)/(n))=k pi, find the value of k