Question

evaluate: tan (2 cot^-1 x)​

Answer 1

${cot}^{ - 1} x = {tan}^{ - 1} \frac{1}{x}$

Now,$2 {tan}^{ - 1} x = {tan}^{ - 1} \frac{2x}{1 - {x}^{2} }$

Thus,

$tan(2 {cot}^{ - 1} x) \\ = tan(2 {tan}^{ - 1} \frac{1}{x} ) \\ = tan( {tan}^{ - 1} \frac{2x}{1 - {x}^{2} } ) \\ = \frac{2x}{1 - {x}^{2} }$