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

Steps to solve 4cosA.cosB.cosC as the sum of four cosines.

Given that

=4cosA.cosB.cosC

=2cosA(2cosB.cosC)

{cos(A+B)+cos(A-B)=2cosA.cosB}

=2cosA{cos(B+C)+cos(B-C)}

=2cosA.cos(B+C)+2cosA.cos(B-C)

=cos(A+B+C)+cos(B+C-A)+cos(B-C+A)+cos(B-C-A)

Hence this is the sum of four cosine expression.

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