Question

What is the value of $2tan^-1 (5) + tan^-1 (5/12)$?

Answer 1

${ \bold{ \green{ \underline{ \underline{ ANSWER}} : - }}}$

${ \bold{ = 2 {tan}^{ - 1} (5) + {tan}^{ - 1} ( \frac{5}{12}) }} \\ \\ { \bold{ = {tan}^{ - 1} ( \frac{10}{ - 24}) + {tan}^{ - 1}( \frac{5}{12} ) }} \\ \\ { \bold{ = {tan}^{ - 1}( - \frac{5}{12}) + {tan}^{ - 1} ( \frac{5}{12}) }} \\ \\ { \bold{ = - {tan}^{ - 1} ( \frac{5}{12} ) + {tan}^{ - 1}( \frac{5}{12} ) }} \\ \\ { \bold{ = 0 }} \\ \\ \\ \\ { \bold{ \red{ \underline{ \underline{ Used \: property}} : - }}} \\ \\ { \bold{ \pink{(1) \: 2{tan}^{ - 1}(x) = { \tan}^{ - 1} ( \frac{2x}{1 - {x}^{2} </strong><strong>}</strong><strong>)</strong><strong> }}} \\ \\ { \bold{ \pink{(2) \: {tan}^{ - 1} ( - x) = - {tan}^{ - 1}(x) }}}$