Hello

I have been having more then some trouble proving some identities. Mostly after some time I have found that I've been missing something very simple and I'm sure it's the same with these, but I'd appreciate some help.

The questions I'm working on are in a section dealing with only the following four identities:

$\displaystyle \tan{x} = \dfrac {\sin x}{\cos x}$

$\displaystyle \sin^2{x} + \cos^2{x} = 1$

$\displaystyle \1 + \tan^2{x} = \sec^2{x}$

$\displaystyle \1 + \cot^2{x} = cosec^2{x}$

I can't do either of these

$\displaystyle \cos^4{x} - \sin^4{x} = \cos^2{x} - \sin^2{x} $

$\displaystyle \sin{x} + \cos{x} = \dfrac {\1 – 2 \cos^2x}{\sin x -\cos x}$

A hint at how to approach these would be very welcome.

Thank you