Solve the equation 2arccosx−arcsin(1−2x2)=0 for all real x.
a. (i) Remove the inverse functions by introducing suitable trigonometric substitutions and obtain an equation solely in x.
b. (ii) Reduce the result of part (i) to a polynomial equation and solve it.
c. (iii) Discuss the admissibility of each root with respect to the domains of the inverse functions used in the original equation.