Question

Giải phương trình sau 

\(\sin x+\cos 2x=1.   \)

Answer 1

\(\sin x+\cos 2x=1.\)

\(\sin x+\cos 2x=1\Leftrightarrow \sin x+1-2\sin ^{2} x=1\Leftrightarrow \sin x-2\sin ^{2} x=0 \)
\(\Leftrightarrow \left[\begin{array}{l} {\sin x=0} \\ {\sin x=\frac{1}{2} } \end{array}\right. \Leftrightarrow \left[\begin{array}{l} {x=k\pi } \\ {x=\frac{\pi }{6} +k2\pi } \\ {x=\frac{5\pi }{6} +k2\pi } \end{array}\right. \, \, \left(k\in {\rm Z}\right).  \)