Saved Bookmarks
| 1. |
LetA and B be obtuse angles such thatsinA=(4)/(5)andcosB=-(12)/(13). |
|
Answer» `-(63)/(65)` It is given that A and B are obtuse angle `rArrcosA=+-sqrt(1-sin^(2))A=+-sqrt(1-(16)/(25))=-(3)/(5)` Negative sign is taken for cos A SINCE A being obtuse lies in second quadrant. `sinB=+-sqrt(1-cos^(2)B)=+-sqrt(1-((-12)/(13))^(2))` `=sqrt((169-144)/(169))=(5)/(13)` Positive sign is taken since , sin B is positive in second quadrant . `rArrcosA=(-3)/(5)andsinB=(3)/(13)` `thereforesin(A+B)=sinAcosB+cosAsinB` `=(4)/(5)XX((-12)/(13))+(-3)/(5)xx((5)/(13))=-(48)/(65)-(15)/(65)` `=(-48-15)/(65)=(-63)/(65)` |
|