Difference of Fourth Powers of Cosine and Sine/Proof 2
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Theorem
- $\sin^4 x - \cos^4 x = \sin^2 x - \cos^2 x$
Proof
| \(\ds \sin^2 x - \cos^2 x\) | \(=\) | \(\ds \left({\sin^2 x - \cos^2 x}\right) \left({\sin^2 x + \cos^2 x}\right)\) | Sum of Squares of Sine and Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sin^4 x - \cos^4 x\) | Difference of Two Squares |
$\blacksquare$