Rewrite the expression as a sum or difference then simplify

Rewrite the expression as a sum or difference, then simplify if possible. 8 sin 6x cos 4x

Solution

8sin6x cos4x

=4(2sin6x cos4x)

2sinAcosB=sin((A+B)_/2)+sin((A-B)_/2)

=4(sin((6x+4x)_/2)+sin((6x-4x)_/2))

=4(sin((10x)_/2)+sin((2x)_/2))

=4(sin(5x) +sin(x))