Question

Prove que : ( 1 + sen^4 alfa - 2sen^2 alfa) (1 + tg^2 alfa) = cos^2 alfa

Answer 1

Boa noite Alcon

(1 - 2sen²(α) + sen(α)⁴) = (1 - sen²(α))² = (cos²(α))² = cos⁴(α)

cos⁴(α) * (1 + tg²(α)) = cos⁴(α) * (cos²(α)/cos²(α) + sen²(α)/cos²(α)) =

cos⁴(α) * (cos²(α) + sen²(α)(cos²(α)) =

cos⁴(α)*(1/cos²(α)) = cos²(α)