Question

Find the values of a for whch `sin^*(-1)x=|x-a|` will have at least one solution.

Answer 1

(i) When `alt0`
In this case, y = a-x must pass through `(1,pi/2)`
`thereforepi/2=a-1rArra=1+pi/2`
(ii) When `alt0`

In this case,
`y=x-a" must pass though "(1,pi/2)`
`pi/2=1-a`
`a=1-pi/2`
For at least on solution.
`1-pi/2leale1+pi/2`