InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
सिद्ध कीजिए `(tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+tan theta+cot theta=1+sec thetacosec theta.` |
|
Answer» यहाँ `L.H.S. =(tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)` `=(tan theta)/(1-(1)/(tantheta))+((1)/(tan theta))/(1-tan theta)=(tan theta)/((tan theta-1)/(tan theta))+(1)/(tan theta(1-tan theta))` `=(tan ^(2)theta)/(tan theta^(-1))+(1)/(tan theta(1-tan theta))=(tan ^(2)theta)/(tan theta-1)-(1)/(tan theta(tan theta-1))` `=(tan ^(3)theta-1)/(tan theta(tan theta-1))=((tan theta-1)(tan ^(2)theta+tan theta+1))/(tan theta(tan theta-1))` `(tan ^(2)theta+tan theta+1)/(tan theta)=(tan ^(2)theta)/(tan theta)+(tan theta)/(tan theta)+(1)/(tan theta)` `=tan theta+1+cot theta=(1+tan theta+cot theta)` `=1+(sin theta)/(cos theta)+(cos theta)/(sin theta)=1+(sin ^(2)theta+cos ^(2)theta)/(sin thetacos theta)=1+(1)/(sin thetacos theta)` `=1+cosec theta sec theta=R.H.S.` |
|