Question

2tan^-1( x) = sin^-1(2x/1+x^2) prove

Answer 1

hope it helps
###Avinash####

Answer 2

hello users........

Here
we have to prove
2tan^-1( x) = sin^-1(2x/1+x^2)

now ,
solution:-
know that
tan^-1(tan x) = x
& (2tan t )/1+ tan²t = sin 2t

now
Taking LHS
= 2tan^-1( x)
put x= tan t
here
2tan^-1(tan t) = 2t

now
solving RHS
sin^-1(2x/1+x^2) = sin^-1 {(2tan t )/1+ tan²t}
=> sin^-1 (sin 2t) = 2t

hence
LHS = RHS

✡✡ hope it helps ✡✡