We will use trigonometric addition formulas on the right side of an equation:[tex] \sqrt{2} (sinx*cos \frac{ \pi }{4} +cosx*sin \frac{ \pi }{4})=
=\sqrt{2}(sin x* \frac{ \sqrt{2} }{2} + cosx * \frac{ \sqrt{2} }{2}=
[/tex]=sinx + cos x. Equation is true.
