tan(x)/sec(-x)

sec(-x)=sec(x)
so
tan(x)/sec(-x)
=tan(x)/sec(x)

putting tan(x)=sin(x)/cos(x) and sec(x)=1/cos(x),we get

=[sin(x)/cos(x)]/[1/cos(x)]
=[sin(x)/cos(x)]*cos(x)
=sin(x)


I hope it helped.