Kako preverite identiteto 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Odgovor:

Glej spodaj

Pojasnilo:

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

Desna stran# = sek ^ 6tea-tan ^ 6theta #

# = (sec ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3 #-> uporabite razliko dveh kock

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

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

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

# = sek ^ 2tea sek ^ 2 theta + sec ^ 2tetatan ^ 2theta + tan ^ 2tea tan ^ 2 theta #

# = sek ^ 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 #

#=# Leva stran