Hvordan verificerer du identiteten 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Svar:

Se nedenunder

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

Højre side# = Sec ^ 6theta-tan ^ 6theta #

# = (Sec ^ 2-theta) ^ 3- (tan ^ 2theta) ^ 3 #-> brug forskel på to terninger formel

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

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

# = Sek ^ 4theta + sek ^ 2thetatan ^ 2-theta + tan ^ 4theta #

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

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

# = Sec ^ 2thetatan ^ 2-theta + sek ^ 2-theta + sek ^ 2thetatan ^ 2-theta + sek ^ 2thetatan ^ 2thetatan ^ 2-theta #

# = Sec ^ 2thetatan ^ 2-theta + sek ^ 2thetatan ^ 2-theta + sek ^ 2thetatan ^ 2-theta + sek ^ 2thetatan ^ 2-theta #

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

#=# Venstre side