InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Prove each of the following identities : `(i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) ` `(ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta) ` |
|
Answer» (i) On dividing num. and denom. by `cos theta`, we get `LHS=((sec theta+tan theta)+1)/((sec theta+1-tan theta))=((sectheta+tan theta)+(sec^(2)theta-tan^(2)theta))/((sec theta+1-tan theta))` `=((sec theta+tan theta)(1+sectheta-tan theta))/((1+sectheta-tan theta))=(sec theta+tan theta)=((1)/(cos theta)+(sintheta)/(cos theta)).` (ii) On dividing num. and denom. by `cos theta`, we get `LHS =(tantheta+sectheta-1)/(1-sectheta+tantheta)=((sectheta+tantheta)-(sec^(2)theta-tan^(2)theta))/((tantheta-sec theta+1))` `=((sectheta+tantheta)[1-(sectheta-tantheta)])/((tan theta-sectheta+1))=(sec theta+tan theta).` |
|