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A value of x satisfying tan(sec^(-1)x...

A value of x satisfying
`tan(sec^(-1)x)=sin(cos^(-1).(1)/sqrt5)` is

A

`pm (3)/sqrt(5)`

B

`pm sqrt(5)/(3)`

C

`pm sqrt(3/5)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
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^(2)-1)=(2)/sqrt(5)rarrx=pm (3)/sqrt(5)`
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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