Question

Simplificar: E=tgx . tg(60°+ x) . tg(60° - x)

Answer 1

$E=\tan x \cdot \left(\dfrac{\tan 60+\tan x}{1-\tan x\tan 60}\right)\cdot \left(\dfrac{\tan 60-\tan x}{1+\tan x\tan 60}\right)\\ \\ E=\tan x \cdot \left(\dfrac{\sqrt3+\tan x}{1-\sqrt3\tan x}\right)\cdot \left(\dfrac{\sqrt3-\tan x}{1+\sqrt3\tan x}\right)\\ \\ \\ \boxed{\boxed{E=\tan x \cdot \left(\dfrac{3-\tan^2 x}{1-3\tan^2 x}\right)}}$