\(sin2x-cos3x=0\)
\(\Leftrightarrow cos\left(2x-\dfrac{\pi}{2}\right)-cos3x=0\)
\(\Leftrightarrow-2sin\left(\dfrac{5x}{2}-\dfrac{\pi}{4}\right).sin\left(-\dfrac{x}{2}-\dfrac{\pi}{4}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\left(\dfrac{5x}{2}-\dfrac{\pi}{4}\right)=0\\sin\left(\dfrac{x}{2}+\dfrac{\pi}{4}\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{5x}{2}-\dfrac{\pi}{4}=k\pi\\\dfrac{x}{2}+\dfrac{\pi}{4}=k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{10}+\dfrac{k2\pi}{5}\\x=-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
Đúng 1
Bình luận (0)
