Ako si overíte identitu 3sec ^ 2thetan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

odpoveď:

Pozri nižšie

vysvetlenie:

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

Pravá strana# = Sek ^ 6theta-tan ^ 6theta #

# = (S ^ 2Theta) ^ 3- (tan ^ 2Theta) ^ 3 #-> použite rozdiel dvoch vzorcov kocky

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

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

# = Sec ^ 4theta + sek ^ 2thetatan ^ 2theta + tan ^ 4theta #

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

# = sek ^ 2theta (tan ^ 2theta + 1) + sec ^ 2tetan + 2teta + tan2teta (sek ^ 2theta-1) #

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

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

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

#=# Ľavá strana