Respuesta :

Use the identity

[tex]1+\tan ^2x=\sec ^2x[/tex]

Then the expression becomes

[tex]\frac{\sec^2x}{\sec x}=\sec x[/tex]

Now, sec x is the reciprocal of cos x.

[tex]\frac{1+\tan^2x}{\sec x}=\frac{1}{\cos x}[/tex]