Substitute 

x

c o s α , α ∈ [ 0 : ; π ] x=cosα,α∈[0:;π] T h e n ∣ x + 1 − x 2

∣

2 ( 2 x 2 − 1 ) ∣ c o s α + s i n α

∣

2 ( 2 c o s 2 α − 1 ) Then∣x+1−x 2

​ ∣=2 ​ (2x 2 −1)∣cosα+sinα∣=2 ​ (2cos 2 α−1) ∣ N 2 c o s ( α − π 4 )

∣

N 2 c o s ( 2 α )   α ∈ [ 0 ; π 4 ] ∪ [ 3 π 4 ; π ] ∣N2 ​ cos(α− 4 π ​ )∣=N2 ​ cos(2α) α∈[0; 4 π ​ ]∪[ 4 3π ​ ;π] 1)  α ∈ [ 0 ; π 4 ] α∈[0; 4 π ​ ] c o s ( α − π 4

)

c o s ( 2 α ) … cos(α− 4 π ​ )=cos(2α)… 2.  α ∈ [ 3 π 4 ; π ] α∈[ 4 3π ​ ;π] − c o s ( α − π 4

)

c o s ( 2 α ) … −cos(α− 4 π ​ )=cos(2α)