Đáp án:
Giải thích các bước giải:
a.
\(\begin{array}{l}
Pt \to \frac{1}{2}(\cos 7x - \cos 3x) = \frac{1}{2}(\cos 7x - \cos x)\\
\to \cos 3x = \cos x \to \left[ \begin{array}{l}
3x = x + k2\pi \\
3x = - x + k2\pi
\end{array} \right. \to \left[ \begin{array}{l}
x = k\pi \\
x = \frac{{k\pi }}{2}
\end{array} \right.(k \in Z)
\end{array}\)
b.
\(\begin{array}{l}
Pt \to (\sin x + \sin 4x) + (\sin 2x + \sin 3x) = 0\\
\to 2.\sin \frac{{5x}}{2}.\cos \frac{{3x}}{2} + 2.\sin \frac{{5x}}{2}.\cos \frac{x}{2} = 0\\
\to \sin \frac{{5x}}{2}.\left[ {\left( {\cos \frac{{3x}}{2} + \cos \frac{x}{2}} \right)} \right] = 0\\
\to \sin \frac{{5x}}{2}.2.\cos x.\cos \frac{x}{2} = 0\\
\to \left[ \begin{array}{l}
\sin \frac{{5x}}{2} = 0\\
\cos x = 0\\
\cos \frac{x}{2} = 0
\end{array} \right. \to \left[ \begin{array}{l}
\frac{{5x}}{2} = k\pi \\
x = \frac{\pi }{2} + k\pi \\
\frac{x}{2} = \frac{\pi }{2} + k\pi
\end{array} \right. \to \left[ \begin{array}{l}
x = \frac{{k2\pi }}{5}\\
x = \frac{\pi }{2} + k\pi \\
x = \pi + k2\pi
\end{array} \right.(k \in Z)
\end{array}\)
