Show that 'tan ^(-1) (m/n)-tan ^(-1) ((m-n)/(m+n))=pi/4'

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

Prove that tan^-1(1/8)+2tan^-1(1/3)+tan^-1(1/57)=pi/4

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

If a_(1), a_(2), a_(3), ………., a_(n) are in AP with common difference 5 and if a_(i)a_(j) ne -1 for i, j = 1, 2, …….., n, then tan^(-1)((5)/(1+a_(1)a_(2))) + tan^(-1)((5)/(1+a_(2)a_(3))) +……..+ tan^(-1)((5)/(1+a_(n-1)a_(n))) is equal to a) tan^(-1)((5)/(1+a(n)a_(n-1))) b) tan^(-1)((5)/(1+a(n)a_(n))) c) tan^(-1)((5n-5)/(1+a(n)a_(n+1))) d) tan^(-1)((5n-5)/(1+a_(1)a_(n)))

Show that the sum of (m+n)^(th) and (m-n)^(th) terms of an A.P . Is equal to twice the m^(th) term.

Show that the sum of (m+n)^(th) and (m-n)^(th) terms of an A . P is equal to twice the m^ (th) térm.

Show that tan^-1frac(1)(5)+tan^-1frac(1)(7)+tan^-1frac(1)(3)+tan^-1frac(1)(8)=pi/4

If a_1,a_2,a_3,…….a_n is an AP with common difference d then tan[tan^(-1)(d/(1+a_1a_2))+tan^(-1)((d)/(1+a_2a_3))+...+tan^(-1)((d)/(1+a_(n-1)a_n))] is equal to a) ((n-1)d)/(a_1+a_n) b) ((n-1)d)/(1+a_1a_n) c) (nd)/(1+a_1a_n) d) (a_n-a_1)/(a_n+a_1)

prove that (tan(pi/4+x))/(tan(pi/4-x))=((1+tanx)/(1-tanx))^2