Question

Prove that `(a-tanx)/(1+atanx)=tan(tan^(-1)a-x)`?

Answer 1

`(a-tanx)/(1+atanx)=tan(tan^(-1)a-x)`

Explanation:

Let `a=tany`, then `y=tan^(-1)a`

So `(a-tanx)/(1+atanx)`

= `(tany-tanx)/(1+tanytanx)`

= `tan(y-x)`

= `tan(tan^(-1)a-x)`