Answer:
[tex]sec^{4}[/tex] x
Step-by-step explanation:
Using the trigonometric identities
sec x = [tex]\frac{1}{cosx}[/tex], tan x = [tex]\frac{sinx}{cosx}[/tex], then
sec²x + [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{sin^2x}{cos^2x}[/tex]
= sec²x + [tex]\frac{sin^2x}{cos^{4x} }[/tex]
= [tex]\frac{1}{cos^2x}[/tex] + [tex]\frac{sin^2x}{cos^{4 } x}[/tex]
= [tex]\frac{cos^2x+sin^2x}{cos^{4}x }[/tex]
= [tex]\frac{1}{cos^{4}x }[/tex] = [tex]sec^{4}[/tex] x
