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cos^(- 1)sqrt((a-x)/(a-b))=sin^(- 1)sqrt...

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

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

Text Solution

Verified by Experts

The correct Answer is:
A, B
`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`
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