[" (इ) "],[qquad tan^(-1)((n)/(n+1))-tan^(-1)(2n+1)=(3 pi)/(4)]

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

tan^(-1)((n-5)/(n-6))+tan^(-1)((n+5)/(n+6))=(pi)/(4)

Prove that tan^(-1)((m)/(n))-tan^(-1)((m-n)/(m+n))=(pi)/(4).

tan^(-1)n+cot^(-1)(n+1)=tan^(-1)(n^(2)+n+1)

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

tan^(-1)""(m)/(n)-tan^(-1)""(m-n)/(m+n) is equal to a) tan^(-1)""(n)/(m) b) tan^(-1)""(m+n)/(m-n) c) (pi)/(4) d) tan^(-1)((1)/(2))

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to tan^(-1)(sqrt(n))-(pi)/(4)tan^(-1)(sqrt(n+1))-(pi)/(4)tan^(-1)(sqrt(n))(d)tan^(-1)(sqrt(n)+1)

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

For n in N ,if tan^(-1)((1)/(3))+tan^(-1)((1)/(4))+tan^(-1)((1)/(5))+tan^(-1)((1)/(n))=(pi)/(4) ,then (n-2)/(15) is equal to

Prove that underset(r=1)overset(n)sum "tan"^(-1)(2r)/(r^(4)+r^(2)+2)="tan"^(-1)(n^(2)+n+1)-(pi)/(4)