13) \(sinxsin3x=\dfrac{1}{2}cos2x\)
\(\Leftrightarrow\dfrac{1}{2}\left(cos2x-cos4x\right)=\dfrac{1}{2}cos2x\)
\(\Leftrightarrow cos2x-cos4x=cos2x\)
\(\Leftrightarrow cos4x=0\)
\(\Leftrightarrow4x=\dfrac{\pi}{2}+k\pi\)
\(\Leftrightarrow x=\dfrac{\pi}{8}+\dfrac{k\pi}{8}\)( k∈Z)
b) \(\left(2sin\dfrac{x}{3}-1\right)tanx=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2sin\dfrac{x}{3}-1=0\\tanx=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\dfrac{x}{3}=\dfrac{1}{2}\\x=k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{x}{3}=\dfrac{\pi}{6}+k2\pi\\x=k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+\dfrac{k2\pi}{3}\\x=k\pi\end{matrix}\right.\)\(\left(k\in Z\right)\)
Chúc bạn học tốt^^
