We are to prove that,
[tex]\cos 2x=\cos ^2x-\sin ^2x[/tex]
Apply the angle-sum identity for cosine to cos (x + x),
Therefore,
[tex]\cos 2x=\cos (x+x)[/tex][tex]\begin{gathered} \cos (x+x)=\cos x\cos x-\sin x\sin x \\ \cos (x+x)=\cos x\times\cos x-\sin x\times\sin x \\ \cos (x+x)=\cos ^2x-\sin ^2x \end{gathered}[/tex]
Hence, with the above prove it has been shown that they are equal.
