Miten varmistat 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Vastaus:

Katso alempaa

Selitys:

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

Oikea puoli# = S ^ 6theta-tan ^ 6theta #

# = (S ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3 #-> kahden kuution kaavan erotus

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

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

# = S ^ 4theta + s ^ 2thetatan ^ 2theta + tan ^ 4theta #

# = sek ^ 2theta sek ^ 2 theta + s ^ 2thetatan ^ 2theta + tan ^ 2theta tan ^ 2 theta #

# = sek ^ 2theta (tan ^ 2theta + 1) + sek ^ 2thetat ^ 2theta + tan ^ 2theta (sek ^ 2theta-1) #

# = S ^ 2thetatan ^ 2theta + s ^ 2theta + s ^ 2thetatan ^ 2theta + s ^ 2thetatan ^ 2thetatan ^ 2theta #

# = S ^ 2thetatan ^ 2theta + s ^ 2thetatan ^ 2theta + s ^ 2thetatan ^ 2theta + s ^ 2thetatan ^ 2theta #

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

#=# Vasen puoli