Step-by-step explanation:
[tex] { \cos}^{2} 45 \degree + { \sin}^{2} 60 + { \sin}^{2} 30 \degree \\ = \bigg( \frac{1}{ \sqrt{2} } \bigg)^{2} + \bigg( \frac{ \sqrt{3} }{ 2} \bigg)^{2} + \bigg( \frac{1}{2} \bigg)^{2} \\ \\ = \frac{1}{2} + \frac{3}{4} + \frac{1}{4} \\ \\ = \frac{2}{4} + \frac{3}{4} + \frac{1}{4} \\ \\ = \frac{2 + 3 + 1}{4} \\ \\ = \frac{6}{4} \\ \\ = \frac{3}{2} \\ \\ = 1 \frac{1}{2} \\ [/tex]
