Jak si ověřujete identitu 3sec ^ 2thatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Odpovědět:

Viz. níže

Vysvětlení:

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

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

# = (sec ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3 #-> použijte rozdíl dvou krychlových vzorců

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

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

# = sec ^ 4theta + sec ^ 2thatan ^ 2theta + tan ^ 4theta #

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

# = sec ^ 2theta (tan ^ 2theta + 1) + sec ^ 2theta + 2theta + 2 ^ theta (sec ^ 2theta-1) #

# = sec ^ 2thatan ^ 2theta + sec ^ 2theta + sec ^ 2tetatan ^ 2theta + sec ^ 2tetatan ^ 2theta-tan ^ 2theta # 2

# = sec ^ 2thatan ^ 2theta + sec ^ 2tetatan ^ 2theta + sec ^ 2tetatan ^ 2theta + sec ^ 2theta-tan ^ 2theta # 2

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

#=# Levá strana