Come si verifica l'identità 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Risposta:

Vedi sotto

Spiegazione:

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

Lato destro# = Sec ^ 6theta-tan ^ 6theta #

# = (Sec ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3 #-> usa la differenza della formula a due cubetti

# = (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 ^ ^ 2thetatan 2theta #

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

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

#=# Lato sinistro