(tg (a) ^2 — sin (a) ^2) / (cos (a) ^2 — ctg (a) ^2)=-tg

(tg²α — sin²α) / (cos²α — ctg²α)=-tg⁶α (sin²α/cos²α) — sin²α) / (cos²α — (cos²α/sin²α)=-tg⁶α (sin²α — sin²α·cos²α) /cos²α) / (cos²α·sin²α — cos²α) /sin²α)=-tg⁶α (sin²α · (1 — cos²α) /cos²α) / (-cos²α· (1 — sin²α) /sin²α)=-tg⁶α (sin²α ·sin²α/cos²α) / (-cos²α·cos²α/sin²α)=-tg⁶α (sin²α ·sin²α ·sin²α) / (-cos²α·cos²α·cos²α)=-tg⁶α-tg⁶α ≡-tg⁶αтождество доказано