" (iv) "tan^(-1)(n)/(n+1)-tan^(-1)(2n+1)=(3 pi)/(4)(UP2009)

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)((n-m)/(n+m))=[(pi)/(4)(m)/(n)>;-1(-3 pi)/(4)(m)/(n)<-1

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

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

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))

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

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

sum_(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1))) is equal to a) tan^(-1)(2^n) b) tan^(-1)(2)^n-pi/4 c) tan^(-1)(2^(n+1)) d) tan^(-1)(2^(n+1))-pi/4

sum_(n=1)^(oo)(tan^(-1)((4n)/(n^(4)-2n^(2)+2))) is equal to ( A) tan^(-1)(2)+tan^(-1)(3)(B)4tan^(-1)(1)(C)(pi)/(2)(D)sec^(-1)(-sqrt(2))