¿Cómo verifica la identidad 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Responder:

Vea abajo

Explicación:

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

Lado derecho# = sec ^ 6theta-tan ^ 6theta #

# = (sec ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3 #-> Usa la diferencia de la fórmula de dos cubos.

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

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

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

#=# Lado izquierdo