[tex]\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad\qquad csc(\theta)=\cfrac{1}{sin(\theta)}
\\\\\\
sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\
-------------------------------\\\\
tan(x)[cos(x)-sin(x)]\implies \cfrac{sin(x)}{cos(x)}\left[ \cfrac{1}{sin(x)}-sin(x) \right]
\\\\\\
\cfrac{sin(x)}{cos(x)}\left[ \cfrac{1-sin^2(x)}{sin(x)}\right]\implies \cfrac{sin(x)}{cos(x)}\left[ \cfrac{cos^2(x)}{sin(x)}\right]\implies cos(x)[/tex]
