Express cos2A+cos2B+cos2C+cos2(A+B+C) as product of three cosines.

Steps tp solve express cos2A+cos2B+cos2C+cis2(A+B+C) as product of three cosines.

=cos2A+cos2B+cos2C+cos2(A+B+C)

={cos2A+cos2B}+{cos2C+cos2(A+B+C)}

=2cos(2A+2B)/2.cos(2A-2B)/2+2cos(2C+2(A+B+C))/2.cos(2C-2(A+B+C))/2

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

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

=2cos(A+B){2cos(A+B+2C-A-B)/2.cos(A-B-A-B-2C)/2}

=4cos(A+B).cos(C+A).cos(B+C)

Hence this is the product of three cosine expression.

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