Question

Evaluate: tan `[ 2 tan^-1  (1)/(2) – cot^-1 3]`

Answer 1

tan `[ 2 tan^-1  (1)/(2) - cot^-1 3]`

= tan `[tan^-1((2xx(1)/(2))/(1-(1/2)^2]) – cot^-1 3]`

= tan `[tan^-1{(1)/(1-(1)/(4)}} - tan^-1  1/3]`

= tan `[tan^-1  4/3 - tan^-1  (1)/(3)]`

= tan `[tan^-1 (((4)/(3) - (1)/(3))/(1+(4)/(9)))]`

= tan `[tan^-1 (((4 -1)/(3))/((9+4)/(9)))]`

= tan `[tan^-1  (1/(13/9))]`

= tan `[tan^-1 ((9)/(13)) ]`

= `(9)/(13)`