The value of x where `xgt0 and tan(sec^(-1)(1/x))=sin(tan^(-1)2)` isA. `sqrt(5)`B. `sqrt(5)/(3)`C. 1D. `2/3`

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

1.	The value of x where `xgt0 and tan(sec^(-1)(1/x))=sin(tan^(-1)2)` isA. `sqrt(5)`B. `sqrt(5)/(3)`C. 1D. `2/3`
Answer» We have `tan(sec^(-1)(1)/(x))=sin(tan^(-1)2)` `rarr tan^(-1)sqrt(1-x^(2))/(x)=sin(sin^(-1))(2)/sqrt(5)` `rarr sqrt(1-x^(2))/(x)=(2)/sqrt(5)rarr(1)/(x^(2))-1=4/5` `rarr(1)/(x^(2))=9/5rarrx=sqrt(5)/(3)`

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