Prove the identity: 1.3arccosx - arccos (3x - 4x ^ 3) = x, X belongs to [- 1 / 2,1 / 2]

Prove the identity: 1.3arccosx - arccos (3x - 4x ^ 3) = x, X belongs to [- 1 / 2,1 / 2]

To prove 3arccosx arccos (3x-4x ^ 3) = π
Prove 3arccosx = π - arccos (3x-4x ^ 3)
Take the cosine value on the left and use the triple angle formula cos3t = 4 (cost) ^ 3-3cost
The results show that cos3arccosx = 4x ^ 3-3x
The cosine value on the right can be obtained by using the induction formula
cos[π-arccos(3x-4x²)]= -cos[arccos(3x-4x²)]=4x^3-3x
Since arccosx is monotone in - 1 to 1, both sides of the equation are equal