One more, guys.

$\displaystyle sin\hspace{5pt}2t - cot\hspace{5pt} t = - cot\hspace{5pt}t\hspace{5pt}cos\hspace{5pt}2t$

On this one, I made a bit of progress, I think.

Starting from the RHS:

$\displaystyle - \frac{cos t}{sin t} * (2 cos^2 t - 1)$

I think that might be the right direction to start in, but I can't see where it goes from here.

Thanks again!