Question

Prove $\left(\cos ({65}^0-{45}^0)\right)=\sqrt{2}\cos {20}^0$

Answer 1

$\sin {65}^0+\cos {65}^0=\sqrt{2}(\frac{1}{2}\sin {65}^0+\frac{1}{\sqrt{2}}\cos {65}^0)$
$=\sqrt{2}\left(\cos ({65}^0-{45}^0)\right)=\sqrt{2}\cos {20}^0$