InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
सरलतम रूप में लिखिए - `tan^(-1).(sqrt(1+x^(2))-1)/(x), x ne 0` |
|
Answer» माना `x=tan theta, " तब "theta=tan^(-1)x, theta in (-(pi)/(2),(pi)/(2))` `therefore" "tan^(-1).(sqrt(1+x^(2))-1)/(x)` `=tan^(-1)[(sqrt(1+tan^(2)theta)-1)/(tan^(2)theta)]` `=tan^(-1)[(sectheta-1)/(tan theta)]," "[because sec theta gt 0, (-(pi)/(2),(pi)/(2))"में "]` `=tan^(-1)[(1-cos theta)/(sin theta)]` `=tan^(-1)[(1-(1-sin^(2).(theta)/(2)))/(2sin.(theta)/(2).cos.(theta)/(2))]` `=tan^(-1)((sin.(theta)/(2))/(cos.(theta)/(2)))` `=tan^(-1)(tan.(theta)/(2))` `[because -(pi)/(2)lt theta lt (pi)/(2) rArr -(pi)/(4)lt(theta)/(2)lt(pi)/(4)]` `=(theta)/(2)=(1)/(2)tan^(-1)x`जो कि अभीष्ट सरलतम रूप है। |
|