Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
sec²x = tan²x + 1
Consider left side
[tex]sec^{4}[/tex] Θ - 4[tex]tan^{4}[/tex] Θ
= (tan²Θ + 1)² - 4[tex]tan^{4}[/tex]Θ ← expand factor using FOIL
= [tex]tan^{4}[/tex]Θ + 2tan²Θ + 1 - 4[tex]tan^{4}[/tex]Θ ← collect like terms
= 1 + 2tan²Θ = right side thus verified
