Question

The value of (sin 45° + cos 45°)³ is _______.

Answer 1

$$\begin{gathered} {\left(\sin 45°+\cos 45°\right)}^3 \\ ={\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)}^3 \\ ={\left(\frac{2}{\sqrt{2}}\right)}^3 \end{gathered}$$
$$\begin{gathered} ={\left(\sqrt{2}\right)}^3 \\ =2\sqrt{2} \end{gathered}$$

The value of (sin 45° + cos 45°)³ is $\underline{2\sqrt{2}}$.