if tan x = 1 where x ∈ (0, π/2) then the value of tan 3x is:

Formula used:

tan 3x = (3tan x - tan³x) / (1 - 3tan²x)

Calculation:

Given that

tan x = 1,

we can substitute this value into the formula:

tan 3x = (3tan x - tan3x) / (1 - 3tan2x)

⇒ tan 3x = [(3 × 1 - (1)³] / [1 - 3 × (1)²]

⇒ tan 3x = (3 - 1) / (1 - 3)

⇒ tan 3x = -1

Therefore, the value of tan 3x is -1.