d, \(cosx-\sqrt{3}sinx-1=0\)
\(\Leftrightarrow\dfrac{1}{2}cosx-\dfrac{\sqrt{3}}{2}sinx=\dfrac{1}{2}\)
\(\Leftrightarrow cos\left(x+\dfrac{\pi}{3}\right)=\dfrac{1}{2}\)
\(\Leftrightarrow x+\dfrac{\pi}{3}=\pm\dfrac{\pi}{3}+k2\pi\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=-\dfrac{2\pi}{3}+k2\pi\end{matrix}\right.\)
e, \(cos3x=1+sin3x\)
\(\Leftrightarrow cos3x-sin3x=1\)
\(\Leftrightarrow cos\left(3x+\dfrac{\pi}{4}\right)=\dfrac{1}{\sqrt{2}}\)
\(\Leftrightarrow3x+\dfrac{\pi}{4}=\pm\dfrac{\pi}{4}+k2\pi\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+\dfrac{\pi}{4}=\dfrac{\pi}{4}+k2\pi\\3x+\dfrac{\pi}{4}=-\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=k2\pi\\3x=-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{k2\pi}{3}\\x=-\dfrac{\pi}{6}+\dfrac{k2\pi}{3}\end{matrix}\right.\)
f, \(sin3x-\sqrt{3}cos3x=\sqrt{2}\)
\(\Leftrightarrow\dfrac{1}{2}sin3x-\dfrac{\sqrt{3}}{2}cos3x=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow sin\left(3x-\dfrac{\pi}{3}\right)=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-\dfrac{\pi}{3}=\dfrac{\pi}{4}+k2\pi\\3x-\dfrac{\pi}{3}=\pi-\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7\pi}{36}+\dfrac{k2\pi}{3}\\x=\dfrac{13\pi}{36}+\dfrac{k2\pi}{3}\end{matrix}\right.\)
