Kako provjeriti identitet sec ^ 4theta = 1 + 2tan ^ 2theta + tan ^ 4theta?

Odgovor:

Dokaz ispod

Obrazloženje:

Prvo ćemo dokazati # 1 + tan ^ 2theta = sec ^ 2theta #:

# sin ^ 2theta + cos ^ 2theta = 1 #

# sin ^ 2 theta / cos ^ 2theta + cos ^ 2theta / cos ^ 2theta = 1 / cos ^ 2theta #

# tan ^ 2theta + 1 = (1 / costheta) ^ 2 #

# 1 + tan ^ 2theta = sec ^ 2theta #

Sada možemo dokazati vaše pitanje:

# Sek ^ 4theta #

# = (S ^ 2 theta) ^ 2 #

# = (1 + 2 theta tan ^) ^ 2 #

# = 1 + 2tan ^ theta + tan ^ 4theta #