For sin2x+cosx=0,\displaystyle {\sin{{2}}}{x}+{\cos{{x}}}={0}, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation in the interval [0,2π).\displaystyle {\left[{0},{2}\pi\right)}.
The answers are
x1=\displaystyle {x}_{{1}}=   ,
x2=\displaystyle {x}_{{2}}=   ,
x3=\displaystyle {x}_{{3}}=   and
x4=\displaystyle {x}_{{4}}=  
with x1<x2<x3<x4\displaystyle {x}_{{1}}\lt{x}_{{2}}\lt{x}_{{3}}\lt{x}_{{4}}.