Question

Simplify `(tan(theta-beta)+tanbeta)/(1-tan(theta-beta)tanbeta)`?

Answer 1

Please see below.

Explanation:

Recall `tan(A+B)=(tanA+tanB)/(1-tanAtanB)` ............(1)

Let `A=theta-beta` and `B=beta`

and then `A+B=theta-beta+beta=theta`

putting these in (1)

`(tan(theta-beta)+tanbeta)/(1-tan(theta-beta)tanbeta)= tantheta`