A) \[\frac{56}{65}\]
B) \[-\frac{56}{65}\]
C) \[\frac{16}{65}\]
D) \[-\frac{16}{65}\]
Correct Answer: D
Solution :
We have \[\sin A=\frac{4}{5}\] and \[\cos B=-\frac{12}{13}\] Now, \[\cos \,(A+B)=\cos A\,\cos B-\sin A\,\sin B\] \[=\sqrt{1-\frac{16}{25}}\,\left( -\frac{12}{13} \right)-\frac{4}{5}\sqrt{1-\frac{144}{169}}\] \[=-\frac{3}{5}\times \frac{12}{13}-\frac{4}{5}\,\left( -\frac{5}{13} \right)=-\frac{16}{65}\] (Since A lies in first quadrant and B lies in third quadrant).
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