[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\\\\
sec(\theta)=\cfrac{1}{cos(\theta)}
\\\\
-----------------------------\\\\
cos(t)[sec(t)-cos(t)]\implies cos(t)sec(t)-cos(t)cos(t)
\\\\\\
cos(t)\cdot \cfrac{1}{cos(t)}-cos^2(t)\implies 1-cos^2(t)\implies \boxed{sin^2(t)}[/tex]
