How to rewrite sin(x)cos(x) with a single trigonometric function?

1 Answer
Ben
Mar 13, 2018

The re-write is #sin(2x)/2#

Explanation:

There is a double angle identity for #sin(2x)# where:

#sin(2x)=2sin(x)cos(x)#

since we have #sin(x)cos(x)# to deal with, we can rearrange the identity to match up:

#sin(2x)/2=(cancel(2)sin(x)cos(x))/cancel(2)#

#sin(2x)/2=sin(x)cos(x)#

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