A) \[\frac{-56}{61}\]
B) \[\frac{-56}{65}\]
C) \[\frac{1}{65}\]
D) \[-56\]
Correct Answer: B
Solution :
We have \[\sin \theta =\frac{12}{13}\] \[\cos \theta =\sqrt{1-{{\sin }^{2}}\theta }=\sqrt{1-{{\left( \frac{12}{13} \right)}^{2}}}=\frac{5}{13}\] and \[\cos \phi =\frac{-3}{5},\,\sin \phi =\sqrt{1-\frac{9}{25}}=\frac{-4}{5},\] \[\left[ \because \,\,\pi <\phi <\frac{3\pi }{2} \right]\] Now, \[\sin (\theta +\phi )=\sin \theta .\cos \,\phi +\cos \theta .\sin \phi \] \[=\left( \frac{12}{13} \right)\left( \frac{-3}{5} \right)+\left( \frac{5}{13} \right)\left( \frac{-4}{5} \right)=\frac{-36}{65}-\frac{20}{65}=\frac{-56}{65}\]
You need to login to perform this action.
You will be redirected in
3 sec
