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9) $sin(2x+\frac{\pi}{6})=-sin(x+\frac{\pi}{4})⇔sin(2x+\frac{\pi}{6})=sin(-x-\frac{\pi}{4})$
$⇔\left[\begin{matrix} 2x+\frac{\pi}{6}=-x-\frac{\pi}{4}+k2\pi\\ 2x+\frac{\pi}{6}=\pi+x+\frac{\pi}{4}+k2\pi\end{matrix}\right.⇔\left[\begin{matrix} 3x=-\frac{5\pi}{12}+k2\pi\\ x=\frac{13\pi}{12}+k2\pi\end{matrix}\right.⇔\left[\begin{matrix} x=-\frac{5\pi}{36}+k\frac{2\pi}{3}\\ x=\frac{13\pi}{12}+k2\pi\end{matrix}\right. (k∈\mathbb{Z})$
10) $sin(2x+\frac{\pi}{4})=cosx⇔sin(2x+\frac{\pi}{4})=sin(\frac{\pi}{2}-x)$
$⇔\left[\begin{matrix} 2x+\frac{\pi}{4}=\frac{\pi}{2}-x+k2\pi\\ 2x+\frac{\pi}{4}=\pi+x-\frac{\pi}{2}+k2\pi\end{matrix}\right.⇔\left[\begin{matrix} 3x=\frac{\pi}{4}+k2\pi\\ x=\frac{\pi}{4}+k2\pi\end{matrix}\right.⇔\left[\begin{matrix} x=\frac{\pi}{12}+k\frac{2\pi}{3}\\ x=\frac{\pi}{4}+k2\pi\end{matrix}\right. (k∈\mathbb{Z})$
11) $sin3x=-cos(x+\frac{\pi}{6})⇔sin3x=cos(\pi-x+\frac{\pi}{6})⇔sin3x=sin[\frac{\pi}{2}-(-x+\frac{7\pi}{6})]⇔sin3x=sin(x-\frac{2\pi}{3})$
$⇔\left[\begin{matrix} 3x=x-\frac{2\pi}{3}+k2\pi\\ 3x=\pi+\frac{2\pi}{3}-x+k2\pi\end{matrix}\right.⇔\left[\begin{matrix} 2x=-\frac{2\pi}{3}+k2\pi\\ 4x=\frac{5\pi}{3}+k2\pi\end{matrix}\right.⇔\left[\begin{matrix} x=-\frac{\pi}{3}+k\pi\\ x=\frac{5\pi}{12}+k\frac{\pi}{2}\end{matrix}\right.(k∈\mathbb{Z})$
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