The period of F(x)=sin|sinx|+sin|cosx| is

Answer 1

The function F(x) is periodic with period 2π since it is trivial to check that

F(x+2π)=sin|sin(x+2π)|+sin|cos(x+2π)|=sin|sin(x)|+sin|cos(x)|=F(x) where we used that the functions sin and cos have period 2π.