Question

cos 22x -1 - cosx =√3/2 -sin 22x

Answer 1

$cos^22x-1-cosx= frac{sqrt3}{2}-sin^22x\\underbrace {(cos^22x+sin^22x)} _{1}-1-cosx=frac{sqrt3}{2}\\cosx=-frac{sqrt3}{2}\\x=pm arccos(-frac{sqrt3}{2})+2pi n,; nin Z\\x=pm (pi -frac{pi}{6})+2pi n=pm frac{5pi}{6}+2pi n,; nin Z$