Question

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

Answer 1

ANSWER:-

$\sf\red{Let x = tan \theta .}$ $\sf\red{Then\: </p><p>\theta = {tan}^{-1} x. \: We \:have}$

$\sf\red{RHS = {tan}^{ - 1} ( \frac{3x - {x}^{3} }{1 - {3x}^{2} } ) = {tan}^{ - 1} ( \frac{3tan \theta- {tan}^{3} \theta}{1 - {3tan}^{2} }\theta )}$

$\sf\red{{tan}^{ - 1} (tan3 \theta) = 3 \theta = {3tan}^{ - 1} x = {tan}^{ - 1} x + 2 {tan}^{ - 1} x}$

$\sf\red{ {tan}^{ - 1} x + {tan}^{ - 1} \frac{2x}{1 - {x}^{2} } = LHS}$