Answer:
[tex]sec^2(x)[/tex]
Step-by-step explanation:
we have the expression
[tex]\frac{sin^2(x)+cos^2(x)}{cos^2(x)}[/tex]
we know that
[tex]sin^2(x)+cos^2(x)=1[/tex] ----> trigonometric identity
and
[tex]sec(x)=\frac{1}{cos(x)}[/tex]
so
[tex]sec^2(x)=\frac{1}{cos^2(x)}[/tex]
substitute in the expression
[tex]\frac{sin^2(x)+cos^2(x)}{cos^2(x)}=(1)(sec^2(x))=sec^2(x)[/tex]
