Question

Prove the following result

`tan(cos^-1  4/5+tan^-1  2/3)=17/6`

Answer 1

LHS=`tan(cos^-1  4/5+tan^-1  2/3)=tan(tan^-1  sqrt(1-(4/5)^2)/(4/5)+tan^-1  2/3)`    `[thereforecos^-1x=tan^-1(sqrt(1-x^2)/x)]`

`=tan(tan^-1  3/4+tan^-1  2/3)`

`=tan[tan^-1((3/4+2/3)/(1-3/4xx2/3))]`      `[thereforetan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))]`

`=tan[tan^-1((17/12)/(6/12))`

`=tan[tan^-1  17/6]`

`=17/6=`RHS