Hoe verifieer je de identiteit 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Antwoord:

Zie hieronder

Uitleg:

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

Rechter zijde# = ^ Sec 6theta-tan ^ 6theta #

# = (Sec ^ 2 theta) ^ 3- (tan ^ 2 theta) ^ 3 #-> gebruik verschil van twee kubussen formule

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

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

# = ^ Sec 4theta + s ^ ^ 2thetatan 2teta + 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 2teta ^ + ^ sec 2teta + s ^ ^ 2thetatan 2teta + s ^ ^ 2thetatan 2thetatan ^ 2teta #

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

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

#=# Linkerkant