UPSC NDA I 2014 Mathematics Paper

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