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If cot(cos^(-1)x)=sec{tan^(-1)(a)/sqrt(b...

If `cot(cos^(-1)x)=sec{tan^(-1)(a)/sqrt(b^(2)-a^(-2))}` then x equals

A

`(b)/(sqrt(2b^(2)-a^(2)))`

B

`(a)/(sqrt(2b^(2)-a^(2)))`

C

`(sqrt(2b^(2)-a^(2)))/(a)`

D

`(sqrt(2b^(2)-a^(2)))/(b)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `cot(cos^(-1)x)=sec("tan"^(-1)(a)/(sqrt(b^(2)-a^(2))))`
`thereforecot[cot^(-1)((x)/(sqrt(1-x^(2))))]=sec["sec"^(-1)((b)/(sqrt(b^(2)-a^(2))))]`
`rArr(x)/(sqrt(1-x^(2)))=(b)/(sqrt(b^(2)-a^(2)))`
`rArrx^(2)(b^(2)-a^(2))=b^(2)-b^(2)-x^(2)`
`rArrx^(2)(2b^(2)-a^(2))=b^(2)`
`rArrx=+-(b)/(sqrt(2b^(2)-a^(2)))`
`rArrx=(b)/(sqrt(2b^(2)-a^(2)))`
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