\(\displaystyle{{\sin}^{{2}}{A}}+{{\sin}^{{4}}{A}}={1}\)

\(\displaystyle{{\sin}^{{4}}{A}}={1}-{{\sin}^{{2}}{A}}\)

\(\displaystyle{{\sin}^{{2}}{A}}{{\sin}^{{2}}{A}}={{\cos}^{{2}}{A}}\)

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

\(\displaystyle{{\sin}^{{2}}{A}}-{{\sin}^{{2}}{A}}{{\cos}^{{2}}{A}}={{\cos}^{{2}}{A}}\)

\(\displaystyle{{\sin}^{{2}}{A}}={{\cos}^{{2}}{A}}+{{\sin}^{{2}}{A}}{{\cos}^{{2}}{A}}\)

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

\(\displaystyle{1}+{{\sin}^{{2}}{A}}={\frac{{{{\sin}^{{2}}{A}}}}{{{{\cos}^{{2}}{A}}}}}\)

\(\displaystyle{1}+{{\sin}^{{2}}{A}}={{\tan}^{{2}}{A}}\)

\(\displaystyle{{\sin}^{{4}}{A}}={1}-{{\sin}^{{2}}{A}}\)

\(\displaystyle{{\sin}^{{2}}{A}}{{\sin}^{{2}}{A}}={{\cos}^{{2}}{A}}\)

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

\(\displaystyle{{\sin}^{{2}}{A}}-{{\sin}^{{2}}{A}}{{\cos}^{{2}}{A}}={{\cos}^{{2}}{A}}\)

\(\displaystyle{{\sin}^{{2}}{A}}={{\cos}^{{2}}{A}}+{{\sin}^{{2}}{A}}{{\cos}^{{2}}{A}}\)

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

\(\displaystyle{1}+{{\sin}^{{2}}{A}}={\frac{{{{\sin}^{{2}}{A}}}}{{{{\cos}^{{2}}{A}}}}}\)

\(\displaystyle{1}+{{\sin}^{{2}}{A}}={{\tan}^{{2}}{A}}\)