Hogyan ellenőrizheti a 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta azonosságát?

Válasz:

Lásd lentebb

Magyarázat:

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

Jobb oldal# = Sec ^ 6theta-tan ^ 6theta #

# = (Sec ^ 2 théta) ^ 3- (tan ^ 2 théta) ^ 3 #-> két kockás képlet különbségének használata

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

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

# = Sec ^ 4theta + sec ^ 2thetatan ^ 2 théta + 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 ^ 2 théta + sec ^ 2 théta + sec ^ 2thetatan ^ 2 théta + sec ^ 2thetatan ^ 2thetatan ^ 2 théta #

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

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

#=# Bal oldal