Answer:
[tex]\cos^2x[/tex]
Step-by-step explanation:
The given expression is:
[tex](\cos x)(\sec x)-\sin^2 x[/tex]
Recall form Pythagorean Identity that;
[tex]\sec x=\frac{1}{\cos x}[/tex]
We apply this property to obtain;
[tex](\cos x)(\frac{1}{\cos x})-\sin^2 x[/tex]
We simplify to get;
[tex]1-\sin^2 x[/tex]
Recall from the Pythagorean identity that;
[tex]1-\sin^2 x=\cos^2x[/tex]
