1.
\(sin\left(2x-\dfrac{\pi}{4}\right)+sin\left(3x+\dfrac{\pi}{3}\right)=0\)
\(\Leftrightarrow2sin\left(\dfrac{5x}{2}-\dfrac{\pi}{24}\right).cos\left(\dfrac{x}{2}+\dfrac{7\pi}{24}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\left(\dfrac{5x}{2}-\dfrac{\pi}{24}\right)=0\\cos\left(\dfrac{x}{2}+\dfrac{7\pi}{24}\right)=0\end{matrix}\right.\)
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2.
\(cos\left(2x-\dfrac{\pi}{4}\right)+sin\left(x+\dfrac{\pi}{4}\right)=0\)
\(\Leftrightarrow cos\left(2x-\dfrac{\pi}{4}\right)+cos\left(\dfrac{\pi}{4}-x\right)=0\)
\(\Leftrightarrow2cos\dfrac{x}{2}.cos\left(\dfrac{3x}{2}-\dfrac{\pi}{4}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos\dfrac{x}{2}=0\\cos\left(\dfrac{3x}{2}-\dfrac{\pi}{4}\right)=0\end{matrix}\right.\)
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