Proof of $\cos 2A={{\cos }^{2}}A-{{\sin }^{2}}A=2{{\cos }^{2}}-1=1-2{{\sin }^{2}}A$

Proof of $\cos 2A={{\cos }^{2}}A-{{\sin }^{2}}A=2{{\cos }^{2}}-1=1-2{{\sin }^{2}}A$

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