a.
\(1+sin\left(3x-\frac{\pi}{3}\right)=sin^2x+cos^2x+2sinx.cosx\)
\(\Leftrightarrow1+sin\left(3x-\frac{\pi}{3}\right)=1+sin2x\)
\(\Leftrightarrow sin\left(3x-\frac{\pi}{3}\right)=sin2x\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-\frac{\pi}{3}=2x+k2\pi\\3x-\frac{\pi}{3}=\pi-2x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow...\)
b.
\(sin2x+cos2x=\frac{\sqrt{6}}{2}\)
\(\Leftrightarrow\sqrt{2}sin\left(2x+\frac{\pi}{4}\right)=\frac{\sqrt{6}}{2}\)
\(\Leftrightarrow sin\left(2x+\frac{\pi}{4}\right)=\frac{\sqrt{3}}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+\frac{\pi}{4}=\frac{\pi}{3}+k2\pi\\2x+\frac{\pi}{4}=\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow...\)
