Use the Pythagorean identity [tex]sin ^{2} x+cos ^{2} x=1[/tex]
to simplify the numerator.
[tex]sin ^{2} x-1=-cos ^{2} x[/tex]
Now use that fact that
[tex]cos(-x)=cos(x)[/tex] to set up the equivalent fraction:
[tex] \frac{sin ^{2}x-1 }{cos(-x)} = \frac{-cos ^{2}x }{cos(x)} [/tex]
Now reduce between the numerator and denominator to get -cos(x)
