## Algebra 2 (1st Edition)

We know that $\cos 2x=\cos^2 x-\sin^2 x$ ...(1) Here, we find two equations obtained form the aboive equation (1). 1) $\cos 2x=1-2 \sin^2 x \implies \cos 2x=\sin^2 x+\cos^2 x-2 \sin^2 x$ and $\cos 2x=1-2 \sin^2 x \implies \cos 2x=\cos^2 x- \sin^2 x$ 2) $\cos 2x=2 \cos^2 x -1 \implies \cos 2x=2 \cos^2 x-(\sin^2 x+cos^2 x)$ and $\cos 2x=\cos^2 x- \sin^2 x$ Hence, it has been verified that all the three formulas are equivalent.