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