b: \(m=sinx+cosx=\sqrt{2}\cdot sin\left(x+\dfrac{\Omega}{4}\right)\)
=>\(\left|m\right|=\sqrt{2}\cdot\left|sin\left(x+\dfrac{\Omega}{4}\right)\right|\)
\(0< =\left|sin\left(x+\dfrac{\Omega}{4}\right)\right|< =1\)
=>\(0< =\sqrt{2}\cdot\left|sin\left(x+\dfrac{\Omega}{4}\right)\right|< =\sqrt{2}\)
=>\(\left|m\right|< =\sqrt{2}\)
Ta có: \(2sinx.cosx=m^2-1\)
\(\left|\left(sinx-cosx\right)\right|=\sqrt{sin^2x-2sinxcosx+cos^2x}\)
\(=\sqrt{1-\left(m^2-1\right)}=\sqrt{2-m^2}\)
\(\Leftrightarrow2-m^2\ge0\)
\(\Leftrightarrow m^2\le2\)
\(\Leftrightarrow\left|m\right|\le\sqrt{2}\)
