dla jakich m nalezacych do R rownanie to jest tozsamoscia

[zuzu]

Dane równanie (2m- \(\displaystyle{ \frac{ \sqrt{5} }{2} ) cos(x+ \frac{x}{4}) =cosx-sinx}\).dla jakich m nalezacych do R rownanie to jest tozsamoscia

[wb]

\(\displaystyle{ cosx-sinx=sin( \frac{\pi}{2}-x)-sinx=2sin \frac{\frac{\pi}{2}-x-x}{2} cos \frac{\frac{\pi}{2}-x+x}{2}= \\ =2sin(\frac{\pi}{4}-x) \frac{\sqrt2}{2}=\sqrt2sin(\frac{\pi}{4}-x)=\sqrt2cos(\frac{\pi}{2}-\frac{\pi}{4}+x)=\sqrt2cos(\frac{\pi}{4}+x) \\ \\ \\ \\ 2m- \frac{\sqrt5}{2}=\sqrt2 \\ ...}\)