`tan^(-1)(tansqrt(1-theta))=sqrt(1-theta)` whenA. `-(pi)/(2) lt theta (pi)/(2)`B. `theta gt (4-pi)/(4)`C. `thetalt (4-pi)/(4)`D. `(4-pi^(2))/(4) lt le 1`

`tan^(-1)(tansqrt(1-theta))=sqrt(1-theta)` whenA. `-(pi)/(2) lt theta

1.	`tan^(-1)(tansqrt(1-theta))=sqrt(1-theta)` whenA. `-(pi)/(2) lt theta (pi)/(2)`B. `theta gt (4-pi)/(4)`C. `thetalt (4-pi)/(4)`D. `(4-pi^(2))/(4) lt le 1`
Answer» Clearly`sqrt(1-theta)` is real if `theta le1` Now `tan^(-1)tansqrt(1-theta)=sqrt(1-theta)` `rarr 0lesqrt(1-theta)lt (pi)/(2) and theta le1` `rarr 0le1-theta lt pi^(2)/(4)and theta le 1` `rarr -1le-theta le(pi^(2))/(4)-1 and theta le1` `rarr 1-(pi^(2))/(4)lt theta le1` and `theta le1 rarr (4-pi^(2))/(4)lt theta le1`

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