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The value of x where xgt0 and tan(sec^(-...

The value of x where `xgt0 and tan(sec^(-1))(1/x)=sin(tan^(-1)2)` is

A

`sqrt(5)`

B

`(sqrt(5))/(3)`

C

1

D

`(2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `tan{sec^(-1)((1)/(x))}=sin(tan^(-1)2)`
`rArrtan("tan"^(-1)(sqrt(1-x^(2)))/(x))=sin("sin"^(-1)(2)/(sqrt(1+2^(2))))`
`[becausesec^(-1)x=("tan"^(-1)sqrt(1-x^(2)))/(x),tan^(-1)x="sin"^(-1)(x)/(sqrt(1+x^(2)))]`
`rArr(sqrt(1-x^(2)))/(x)=(2)/(sqrt(5))rArr4x^(2)=5(1-x^(2))`
`rArrx^(2)=(5)/(9)rArrx=(sqrt(5))/(3)`
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