Look, we have:

\(\displaystyle{{\sin}^{{{2}}}-}{{\cos}^{{{2}}}{x}}={{\sin}^{{{2}}}{x}}+{\left({{\cos}^{{{2}}}{x}}-{{\cos}^{{{2}}}{x}}\right)}-{{\cos}^{{{2}}}{x}}={\left({{\sin}^{{{2}}}{x}}+{\cos}^{{{2}}}\right)}-{2}{{\cos}^{{{2}}}{x}}={1}-{2}{{\cos}^{{{2}}}{x}}\)

\(\displaystyle{{\sin}^{{{2}}}-}{{\cos}^{{{2}}}{x}}={{\sin}^{{{2}}}{x}}+{\left({{\cos}^{{{2}}}{x}}-{{\cos}^{{{2}}}{x}}\right)}-{{\cos}^{{{2}}}{x}}={\left({{\sin}^{{{2}}}{x}}+{\cos}^{{{2}}}\right)}-{2}{{\cos}^{{{2}}}{x}}={1}-{2}{{\cos}^{{{2}}}{x}}\)