A) \[\cos A\cos B=\frac{1}{5}\]
B) \[\sin A\sin B=-\frac{2}{5}\]
C) \[\cos A\cos B=-\frac{1}{5}\]
D) \[\sin A\sin B=-\frac{1}{5}\]
Correct Answer: A
Solution :
\[\cos \,(A-B)=\frac{3}{5}\] \ \[5\,\,\cos A\,\,\cos B+5\,\,\sin A\,\,\sin B=3\] ?..(i) From 2nd relation, \[\sin A\sin B=2\cos A\cos B\] .....(ii) \[\therefore \] \[\cos A\cos B=\frac{1}{5}\] and \[5\,\left( \frac{1}{2}+1 \right)\,\sin A\,\,\sin B=3\].
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