Kako preverite identiteto sec ^ 4theta = 1 + 2tan ^ 2theta + tan ^ 4theta?

Odgovor:

Dokaz spodaj

Pojasnilo:

Najprej bomo dokazali # 1 + tan ^ 2theta = sec ^ 2theta #:

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

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

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

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

Zdaj lahko dokažemo vaše vprašanje:

# sec ^ 4theta #

# = (sec ^ 2theta) ^ 2 #

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

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