hey

need some help with this one please..

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

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

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

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

$\displaystyle \rightarrow$ RHS = LHS

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

many thanks