`cos^(- 1)sqrt((a-x)/(a-b))=sin^(- 1)sqrt((x-b)/(a-b))` is possible ,if

Options

A. `a gt x gt b`
B. `a lt x lt b`
C. `a = x = b`
D. `a gt b` and x takes any value

Answer

A, B

Explanation

`cos^(-1)(sqrt((a-x)/(a-b)))=sin^(-1)(sqrt(1-(a-x)/(a-b)))`
`=sin^(-1)(sqrt((x-b)/(a-b)))`
`therefore` We must have `(a-x)/(a-b)gt 0` and `(x-b)/(a-b)gt 0`
`0 le (a-x)/(a-b)lt 1` and `0 le (x-b)/(a-b)lt 1`
From both, we get `0 le (a-x)/(a-b)lt 1`
`therefore a gt x gt b` or `a lt x lt b`