Pls prove : 2tan-1x = sin-1(2x/1+x2) Share with your friends Share 3 Shruti Tyagi answered this Dear student, To Prove: 2tan-1x=sin-12x1+x2Taking R.H.Ssin-12x1+x2Put x=tanθ ...(1)⇒tan-1x=θ ...(2)from (1)we get, sin-12tanθ1+tan2θBut we know that sin2θ=2tanθ1+tan2θ= sin-1 sin2θ=2θPutting the value of θ from (2)=2tan-1x=L.H.Ssince L.H.S=R.H.SHence proved Regards 9 View Full Answer Muskan Rana answered this Let tan-1x= t tan t = x sin 2t =2sin t cos t =2{x/(1+x2)1/2}{1/(1+x2)1/2} {since, sint = x/1+x2 and cost = 1/1+x2) =2x/1+x2 2t =sin-1(2x/1+x2) 2tan-1x =sin-1(2x/1+x2) Hence, proved. 1 Sahil answered this hope i made myself clear 6
