Wie verifizieren Sie die Identität 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Antworten:

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Erläuterung:

# 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta #

Rechte Seite# = sec ^ 6theta-tan ^ 6theta #

# = (sec ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3 #-> Unterschied zwischen zwei Würfeln verwenden

# = (sec ^ 2theta-tan ^ 2theta) (sec ^ 4theta + sec ^ 2thetatan ^ 2theta + tan ^ 4theta) #

# = 1 * (sec ^ 4theta + sec ^ 2thetatan ^ 2theta + tan ^ 4theta) #

# = sec ^ 4theta + sec ^ 2thetatan ^ 2theta + tan ^ 4theta #

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

# = sec ^ 2theta (tan ^ 2theta + 1) + sec ^ 2thetatan ^ 2theta + tan ^ 2theta (sec ^ 2theta-1) #

# = sec ^ 2thetatan ^ 2theta + sec ^ 2theta + sec ^ 2thetatan ^ 2theta + sec ^ 2thetatan ^ 2theta-tan ^ 2theta #

# = sec ^ 2thetatan ^ 2theta + sec ^ 2thetatan ^ 2theta + sec ^ 2thetatan ^ 2theta + sec ^ 2theta-tan ^ 2theta #

# = 3sec ^ 2thetatan ^ 2theta + 1 #

#=# Linke Seite