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If sintheta=(12)/(13),(0ltthetalt(pi)/(...

If `sintheta=(12)/(13),(0ltthetalt(pi)/(2))and cosphi=-(3)/(5),(piltphilt(3pi)/(2))`. Then , `sin(theta+phi)` will be

A

`(-56)/(61)`

B

`(-56)/(65)`

C

`(1)/(65)`

D

`-56`

Text Solution

Verified by Experts

The correct Answer is:
B
We have ,`sintheta=(12)/(13)`
`costheta=sqrt(1-sin^(2)theta)sqrt(1-((12)/(13))^(2))=(5)/(13)`
and `cosphi=(-3)/(5)`
`sinphi=sqrt(1-(9)/(25))=(-4)/(5) " " [becausepiltphilt(3pi)/(2)]`
Now ,`sin(theta+phi)=sintheta*cosphi+costheta*sinphi`
`=((12)/(13))((-3)/(5))+((5)/(13))((-4)/(5))`
`=(-36)/(65)-(20)/(65)=(-56)/(65)`
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