The fromula:

\(\displaystyle{\cos{{\left({x}\right)}}}={\sin{{\left({90}^{\circ}-{x}\right)}}}\)

Substitute the given angle:

\(\displaystyle{\cos{{\left({72}^{\circ}\right)}}}={\sin{{\left({90}^{\circ}-{72}^{\circ}\right)}}}\)

\(\displaystyle{\cos{{\left({72}^{\circ}\right)}}}={\sin{{\left({18}^{\circ}\right)}}}\)

\(\displaystyle=\frac{{\sqrt{{2}}\sqrt{{{3}-\sqrt{{5}}}}}}{{4}}\)

\(\displaystyle\approx{0.30901}\)

\(\displaystyle{\cos{{\left({x}\right)}}}={\sin{{\left({90}^{\circ}-{x}\right)}}}\)

Substitute the given angle:

\(\displaystyle{\cos{{\left({72}^{\circ}\right)}}}={\sin{{\left({90}^{\circ}-{72}^{\circ}\right)}}}\)

\(\displaystyle{\cos{{\left({72}^{\circ}\right)}}}={\sin{{\left({18}^{\circ}\right)}}}\)

\(\displaystyle=\frac{{\sqrt{{2}}\sqrt{{{3}-\sqrt{{5}}}}}}{{4}}\)

\(\displaystyle\approx{0.30901}\)