Question

Prove the following result:

`tan^-1  1/7+tan^-1  1/13=tan^-1  2/9`

Answer 1

LHS = `tan^-1  1/7+tan^-1  1/13`

`=tan^-1((1/7+1/13)/(1-1/7xx1/13))`     `[becausetan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))`

`=tan^-1((20/91)/(90/91))`

`=tan^-1  2/9=` RHS