Tg α * ctg α - 1 / cos ^2 α

Question

Tg α * ctg α - 1 / cos ^2 α

Answer 1

Tgα*ctgα-1/cos²α=1-1/cos²α=(cos²α-1)/cos²α=(cos²α-(sin²α+cos²α))/cos²α=
=-sin²α/cos²α=-tg²α.