NDA Math Trigonometric Ratios of Angles and Equations

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