2.cos^2x-√3sin2x=√2

2cos ²x-1- √3 sin2x= √2 -1

cos2x- √3 sin2x= √2 -1

$\frac{1}{2}$ cos2x-$\frac{√3}{2}$ sin2x=$\frac{ √2 -1

}{2}$

sin$\frac{\pi}{6}$cos2x-sin2x.cos $\frac{\pi}{6}$=$\frac{ √2 -1

}{2}$

sin($\frac{\pi}{6}$-2x)=$\frac{ √2 -1

}{2}$

$\frac{\pi}{6}$-2x= arcsin($\frac{ √2 -1

}{2}$ )+k2$\pi$ hoặc $\frac{\pi}{6}$-2x= $\pi$ - arcsin($\frac{ √2 -1

}{2}$ )+k2$\pi$

x=$\frac{\pi}{12}$-$\frac{arcsin(\frac{ √2 -1

}{2} )}{2}$ + k$\pi$ hoặc x=$\frac{-5\pi}{12}$+$\frac{arcsin(\frac{ √2 -1

}{2} )}{2}$ + k$\pi$