Question

To Prove :tan-1x +tan-1(2x/1-x^2)=(3x-x^3/1-3x^2)

Answer 1

➡HERE IS YOUR ANSWER⬇

L.H.S.
$= {tan}^{ - 1} x + {tan}^{ - 1} \frac{2x}{1 - {x}^{2} } \\ \\ = {tan}^{ - 1} ( \frac{x + \frac{2x}{1 - {x}^{2} } }{1 - x. \frac{2x}{1 - {x}^{2} } } ) \\ \\ = {tan}^{ - 1} (\frac{ \frac{x(1 - {x}^{2}) + 2x }{1 - {x}^{2} } }{ \frac{(1 - {x}^{2}) - 2 {x}^{2} }{1 - {x}^{2} } } ) \\ \\ = {tan}^{ - 1} ( \frac{3x - {x}^{3} }{1 - 3 {x}^{2} } )$
=RHS (Proved).

■] IMPORTANT FORMULA [■

${tan}^{ - 1} x + {tan}^{ - 1} y \\ \\ = {tan}^{ - 1} (\frac{x + y}{1 - xy})$


⬆HOPE THIS HELPS YOU⬇