Prove that: tan 3x tan 2x tan x = tan 3x − tan 2x − tan x

To Prove this we will use trigonometric formulae of tan (A + B) = (tan A + tan B) / 1 - tan A tan B.

Answer: We can prove tan 3x tan 2x tan x = tan 3x − tan 2x − tan x using trigonometric formulae

Explanation:

We will start by splitting tan 3x

⇒ Let tan 3x = tan ( 2x + x )

Using the trigonometric formula tan(A + B), we get

⇒ tan 3x = tan 2x + tan x / 1 - tan 2x tan x

On solving this equation using cross multiplication, we get

⇒ tan 3x - tan 3x tan 2x tan x = tan 2x + tan x

⇒ tan 3x - tan 2x - tan x = tan 3x tan 2x tan x 

Hence, it is proved that tan 3x tan 2x tan x = tan 3x − tan 2x − tan x.