1.

LetA and B be obtuse angles such thatsinA=(4)/(5)andcosB=-(12)/(13).

Answer»

`-(63)/(65)`
`-(33)/(65)`
`(33)/(65)`
`(63)/(35)`

Solution :`sinA=(4)/(5)andcosB=-(12)/(13)`
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)`


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