<s>[INST] How to prove $\cos^4x - \sin^4x - \cos^2x + \sin^2x$ is always $0$? So I have a small problem here where I have to prove the following :

$$\cos^4x - \sin^4x - \cos^2x + \sin^2x = 0 $$

I know that the 2nd part is always $1$, so I need to prove that the first part also equals $1$. So how should I prove it ?
Edit : Sorry, the equation itself was wrong. I've edited it. 
 [/INST] The edited identity is correct.
Use $a^2 - b^2 = (a+b)(a-b)$ to rewrite $\cos^4 x - \sin^4 x = (\cos^2 x - \sin^2 x)(cos^2 x + \sin^2 x)$.
The second factor is one ($\sin^2 x + \cos^2 x = 1$), reducing the original expression to:
$\cos^2x - \sin^2x - \cos^2x + \sin^2x = 0$ as required.
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