Sinx + sin2x= cosx + cos2x

Đáp án:

Giải thích các bước giải:
\[\begin{array}{l}
\sin x + \sin 2x = \cos x + \cos 2x\\
\Leftrightarrow \sin x – \cos 2x = \cos x – 2\sin x\\
\Leftrightarrow \sin x + 2{\sin ^2}x – 1 = \cos x – 2\sin x.\cos x\\
\Leftrightarrow (2\sin x – 1)(\sin x + 1) – \cos x(1 – 2\sin x) = 0\\
\Leftrightarrow (2\sin x – 1)(\sin x + \cos x + 1) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin x = \frac{1}{2} \Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{6} + k2\pi \\
x = \frac{{5\pi }}{6} + k2\pi
\end{array} \right.\\
\sin x + \cos x = – 1 \Leftrightarrow \sin (x + \frac{\pi }{4}) = \frac{{ – \sqrt 2 }}{2} \Leftrightarrow \left[ \begin{array}{l}
x = \frac{{ – \pi }}{2} + k2\pi \\
x = \pi + k2\pi
\end{array} \right.
\end{array} \right.
\end{array}\]