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Value of x satisfying tan(sec^(- 1)x)=...

Value of x satisfying ` tan(sec^(- 1)x)=sin(cos^(- 1)(1/(sqrt(5))))`

A

`pm sqrt(5)/(3)`

B

`pm (3)/sqrt(5)`

C

`pm sqrt(3)/(5)`

D

`pm 3/5`

Text Solution

Verified by Experts

The correct Answer is:
D
We have
`tan(sec^(-1)x)=sin(cos^(-1)(1)/sqrt(5))`
`rarr sqrt(sec^(2)(sec^(-1)x)-1)=sin(sin^(-1))(2)/sqrt(5)`
`rarr sqrt(x^(-1))=(2)/sqrt(5)rarrx=pm (3)/sqrt(5)`
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