Mathematics

Problem

Let

a\in\mathbb R

be a real parameter. Consider the equation

\arcsin(ax)+\arccos x=\dfrac{\pi}{2}

where

x\in[-1,1]

. a. (i) Rewrite the equation so that it contains only one inverse trigonometric function. b. (ii) Hence obtain the condition on

a

for which the equation has at least one real solution in

x\in[-1,1]

. c. (iii) For every admissible value of

a

found in part (ii), determine the corresponding solution(s) for

x