Which expression is equivalent to tan 2x − tan x 1 + tan 2x tan x? (A) tan x (B) tan 3x (C) tan 2x − 1 1 + tan 2x (D) tan x 1 + tan 2x tan x - HSC - SSCE Mathematics Extension 1 - Question 3 - 2016 - Paper 1

We recall the formula for the tangent of the difference of angles:

$tan(A - B) = \frac{tan A - tan B}{1 + tan A \cdot tan B}$

In this case, we can let (A = 2x) and (B = x). Thus,

$tan(2x - x) = tan(x)$

Therefore, the expression simplifies to:

$tan(x)$

This matches option (A) from the question.