trig identity question

hey

need some help with this one please..

i need to prove that $cot^2 \theta - cos^2 \theta = cot^2 \theta cos^2 \theta$

i took the right hand side and tried to do a similar thing to my text book in proving the question...

this is what I got

$cot^2 \theta cos^2 \theta =$ $(cos^2 \theta - cos^2 \theta.sin^2 \theta) \over(sin^2 \theta)$

$\rightarrow$ $cos^2 \theta\over sin^2\theta$ - $cos^2 \theta \dot sin^2\theta \over sin^2 \theta$

$\rightarrow$ RHS = LHS

first of all is this correct? and second of all what rule gives me my first line?

many thanks :)