a) \(\left(2m-1\right)sinx+1-m=0\Rightarrow sinx=\dfrac{m-1}{2m-1}\)
Pt có nghiệm: \(-1\le\dfrac{m-1}{2m-1}\le1\)
\(\Rightarrow1-2m\le m-1\le2m-1\Rightarrow m\ge\dfrac{2}{3}\)
b) \(\left(m+1\right)sin3x-cos3x=m+2\)
Pt có nghiệm: \(\left(m+1\right)^2+\left(-1\right)^2\ge\left(m+2\right)^2\)
\(\Rightarrow m^2+2m+1+1\ge m^2+4m+4\)
\(\Rightarrow-2m\ge2\Rightarrow m\le-1\)
a, \(\left(2m-1\right)sinx+1-m=0\)
\(\Leftrightarrow sinx=\dfrac{m-1}{2m-1}\)
Phương trình có nghiệm khi:
\(-1\le\dfrac{m-1}{2m-1}\le1\)
\(\Leftrightarrow\left[{}\begin{matrix}m>\dfrac{2}{3}\\m\le0\end{matrix}\right.\)
c) \(msin^2x-sin2x+\left(m+3\right)cos^2x=0\)
\(\Rightarrow m\cdot\dfrac{1-cos2x}{2}-sin2x+\left(m+3\right)\cdot\dfrac{1+cos2x}{2}=0\)
\(\Rightarrow-2sin2x+3cos2x=-3-2m\)
Pt có nghiệm: \(\left(-2\right)^2+3^2\ge\left(3+2m\right)^2\)
\(\Rightarrow m^2+3m-1\ge0\)
\(\dfrac{-3-\sqrt{13}}{2}\le m\le\dfrac{-3+\sqrt{13}}{2}\)
b, \(\left(m+1\right)sin3x-cos3x=m+2\)
Phương trình có nghiệm khi:
\(\left(m+1\right)^2+1^2\ge\left(m+2\right)^2\)
\(\Leftrightarrow m^2+2m+1+1\ge m^2+4m+4\)
\(\Leftrightarrow2m+2\le0\)
\(\Leftrightarrow m\le-1\)
c, \(m.sin^2x-sin2x+\left(m+3\right).cos^2x=0\)
\(\Leftrightarrow2m.sin^2x-2sin2x+2m.cos^2x+6cos^2x=0\)
\(\Leftrightarrow2m-2sin2x+6cos^2x=0\)
\(\Leftrightarrow2sin2x-6cos^2x+3=2m+3\)
\(\Leftrightarrow2sin2x-3cos2x=2m+3\)
Phương trình có nghiệm khi:
\(2^2+3^2\ge\left(2m+3\right)^2\)
\(\Leftrightarrow13\ge4m^2+12m+9\)
\(\Leftrightarrow4m^2+12m-4\le0\)
\(\Leftrightarrow\dfrac{-3-\sqrt{13}}{2}\le m\le\dfrac{-3+\sqrt{13}}{2}\)
