Question

Tìm m để PT có nghiệm: \(2\sin x+m=2\)

Answer 1

\(\Leftrightarrow2\sin x=2-m\)

\(\Leftrightarrow\sin x=\dfrac{2-m}{2}\)

ĐK có nghiệm: \(-1\le\dfrac{2-m}{2}\le1\)

\(\Leftrightarrow-2\le2-m\le2\)

\(\Leftrightarrow-4\le-m\le0\)

\(\Leftrightarrow4\ge m\ge0\)

\(\Leftrightarrow0\le m\le4\)