[tex]\bf sec(x) -cos(x) = tan(x) sin(x)\\\\
-----------------------------\\\\
sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
-----------------------------\\\\
thus
\\\\\\
\cfrac{1}{cos(x)}-cos(x)\implies \cfrac{1-cos^2(x)}{cos(x)}\\\\
-----------------------------\\\\
recall\implies sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\\\\
-----------------------------\\\\
\cfrac{sin^2(x)}{cos(x)}\implies \cfrac{sin(x)}{cos(x)}\cdot sin(x)\implies tan(x)sin(x)[/tex]
