## Trigonometry (11th Edition) Clone

$$\cos^22x-\sin^22x=\cos4x$$
$$X=\cos^22x-\sin^22x$$ Recall the Double-Angle Identity for cosine, which states $$\cos^2A-\sin^2A=\cos2A$$ Therefore, here we can absolutely apply the identity right away with $A=2x$, meaning that $$\cos^22x-\sin^22x=\cos(2\times2x)$$ $$\cos^22x-\sin^22x=\cos4x$$ Therefore, $$X=\cos4x$$ In conclusion, the result is $$\cos^22x-\sin^22x=\cos4x$$