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Prove the following : Express 4cosA.cosB...

Prove the following : Express 4cosA.cosB.cosC as the sum of four cosines.

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4cosAcosBcosC
= 2(2cosAcosB)cosC
= 2[cos(A+B)+cos(A-B)]cosC
= 2cos(A+B)cosC+2cos(A-B)cosC
cos(A+B+C)+cos(A+B-C)+cos(A-B+C)+cos(A-B-C)
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