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Question

In a ΔABC, prove that a cos A+b cos B+c cos C=2a sin B sin C

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Solution

Let asin A=bsin B=csin C=k.Then a=k sin A, b=k sin B, c=k sin CL.H.S=a cos A+b cos B+c cos C=k sin A cos A+k sin B cos B+k sin C cos C=k2 (sin 2A+sin 2B+sin 2C)=k2 (4 sin A sin B sin C)=2k sin A sin B sin C=2a sin B sin C=RHS.


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