Question

Tan 9x - tan 5x/ 1+ tan 9x tan 5x

Answer 1

tan 4x

Explanation:

Note the difference identity for tangent ratio is

tan(x - y) =
`(tanx-tany)/(1+tanxtany)`

Given

`(tan9x-tan5x)/(1+tan9xtan5x)` ← in the form of the right side of the expansion, thus

= tan(9x - 5x)

= tan 4x