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 \[\cos \varphi =\frac{-3}{5},\sin \varphi =\sqrt{1-\frac{9}{25}}=\frac{-4}{5}\], \[\left[ \because \pi <\varphi <\frac{3\pi }{2} \right]\] Now, \[\sin (\theta +\varphi )=\sin \theta .\cos \varphi +\cos \theta .\sin \varphi \] \[=\left( \frac{12}{13} \right)\,\left( \frac{-3}{5} \right)+\left( \frac{5}{13} \right)\,\left( \frac{-4}{5} \right)=\frac{-36}{65}-\frac{20}{65}\]\[=\frac{-56}{65}\].
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