सिद्ध कीजिए -
` 2 tan ^( -1) "" ( 1 ) /(5) = tan ^( -1) "" ( 5 ) /(12) `

Explanation

L.H.S. = ` 2tan ^( -1) "" ( 1 ) /(5) `
` = tan ^( -1) [ (2 xx ( 1 ) /(5))/(1 - (( 1 ) /(5))^2 ) ], " "[ because 2 tan ^( -1) x = tan ^( -1) "" (2x ) /( 1 - x ^ 2 ) ] `
` = tan ^( -1) [ (2//5)/( 1 - ( 1 ) /(25))] `
` = tan ^( -1) [ (2//5)/(24//25)] = tan ^( -1) [ ( 2 )/(5) xx (25 ) /(24) ] `
` tan ^( -1) [ (5 ) /(12)] = `R.H.S.