Question

Sin 36 degrees + cos 36 degrees = square root of 2 cos 9 degrees?

Answer 1

$$\begin{gathered} \sin 36+\cos 36=\sqrt{2}\left(\frac{1}{\sqrt{2}}\sin 36+\frac{1}{\sqrt{2}}\cos 36\right) \\ =\sqrt{2}\left(\sin 45\sin 36+\cos 45\cos 36\right) \\ =\sqrt{2}\left(\cos 45\cos 36+\sin 45\sin 36\right) \\ =\sqrt{2}\cos \left(45-36\right) \\ =\sqrt{2}\cos 9 \\ \mathrm{hence}\mathrm{proved}. \end{gathered}$$