Question

Prove that `tan^-1  2/11 + tan^-1  7/24 = tan^-1  1/2`

Answer 1

`tan^-1"A" + tan^-1"B" = tan^-1 (("A" + "B")/(1 - "AB"))`

`tan^-1 (2/11) + tan^-1 (7/24) = tan^-1 ((2/11 + 7/24)/(1- 2/11 * 7/24))`

= `tan^-1  (((48 + 77)/(11 xxx 24))/((264 - 14)/(11 xx 24)))`

= `tan^-1 (125/250)`

= `tan^-1(1/2)`