Question

Доказать тригонометрическое тождество

Answer 1

(sin²α-1)/cos⁴α+tg²α=(sin²α-(sin²α+cos²α))/cos⁴α+sin²α/cos²α=
=-cos²α/cos⁴α+sin²α/cos²α=-1/cos²α+sin²α/cos²α=(sin²α-1)/cos²α=
=(sin²α-(sin²α+cos²α))/cos²α=-cos²α/cos²α≡-1.