Prove that:

tan 8x – tan6x – tan 2x = tan 8x

tan 6x tan 2x

We have 8x = 6x + 2x

⇒ tan 8x = tan(6x + 2x)

We know that

⇒ tan8x (1 – tan6x tan2x) = tan6x + tan2x

⇒ tan8x – tan8x tan 6x tan2x = tan6x + tan2x

∴ tan8x – tan6x – tan2x = tan8x tan6x tan2x

Hence, proved.