A) \[a\cos A+b\cos B+c\cos C=R\sin A\sin B\sin C\]
B) \[a\cos A+b\cos B+c\cos C=2R\sin A\sin B\sin C\]
C) \[a\cos A+b\cos B+c\cos C=4R\sin A\sin B\sin C\]
D) \[a\cos A+b\cos B+c\cos C=8R\sin A\sin B\sin C\]
Correct Answer: C
Solution :
\[\because \] \[a=2R\sin A,\,\,b=2R\sin B,\,\,c=2R\,\sin C\] \[\therefore \] \[a\cos A+b\cos B+c\cos C\] \[=R[(2\sin A\cos A)+(2\sin B\cos B)+(2\sin C\cos C)]\] \[=R(\sin 2A+\sin 2B+\sin 2C)\]\[=4R\sin A\sin B\sin C.\]
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