To prove that the statements are incorrect, it's enough to show an example, where the given statements are false. As we can see fro the figure for π<x<
3π
2
sin|x|,cos|x|<0, hence sin|x|+cos|x|<0 The first statement is false Similarly for $√{π}sinx2,cosx2<0, hence sinx2+cosx2<0 Statement 2 is also false