w: \(\sin2x-\sqrt3\cdot cos2x=\sqrt3\)
=>\(\sin2x\cdot\frac12-\frac{\sqrt3}{2}\cdot cos2x=\frac{\sqrt3}{2}\)
=>\(\sin\left(2x-\frac{\pi}{3}\right)=\sin\left(\frac{\pi}{3}\right)\)
=>\(\left[\begin{array}{l}2x-\frac{\pi}{3}=\frac{\pi}{3}+k2\pi\\ 2x-\frac{\pi}{3}=\pi-\frac{\pi}{3}+k2\pi\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=\frac23\pi+k2\pi\\ 2x=\pi+k2\pi\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac13\pi+k\pi\\ x=\frac{\pi}{2}+k\pi\end{array}\right.\)
q: \(\sin^4x+cos^4x=1\)
=>\(\left(\sin^2x+cos^2x\right)^2-2\cdot\sin^2x\cdot cos^2x=1\)
=>\(2\cdot\sin^2x\cdot cos^2x=0\)
=>\(\sin x\cdot cosx=0\)
=>\(\left[\begin{array}{l}\sin x=0\\ \cos x=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=k\pi\\ x=\frac{\pi}{2}+k\pi\end{array}\right.\Rightarrow x=\frac{k\pi}{2}\)
