The sides of a triangel are such that `a/(1+m^2+n^2)=b/(m^2+n^2)=c/((1-m^2)(1+n^2))`, prove that `A=2tan^-1 m/n, B=2tan^-1 (mn) and /_\ = (mnbc)/(m^2+n^2)`

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

Prove that: tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=[pi/4; m^(2)/n^(2) > -1

If l, m, n denote the side of a pedal triangle, then (l)/(a ^(2))+(m)/(b^(2))+(n)/(c ^(2)) is equal to

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

If S_n denotes the sum of first n terms of an A.P. such that (S_m)/(S_n)=(m^2)/(n^2),\ t h e n(a_m)/(a_n)= a. (2m+1)/(2n+1) b. (2m-1)/(2n-1) c. (m-1)/(n-1) d. (m+1)/(n+1)

If tanA=m/(m-1)\ a n d tanB=1/(2m-1), then prove that A-B=\ pi/4

If m >1,n in N show that 1^m+2^m+2^(2m)+2^(3m)++2^(n m-m)> n^(1-m)(2^n-1)^mdot

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}

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