How do you use the product to sum formulas to write #6sin(pi/4)cos(pi/4)# as a sum or difference?

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Answer 1 · 2018-02-21T19:11:36

The expression is equal to #3sin(pi/2)#.

Using this formula:

#color(white)=sin(2x)=2sinxcosx#

We can do it backwards:

#color(white)=6sin(pi/4)cos(pi/4)#

#=3(2sin(pi/4)cos(pi/4))#

#=3(sin(2*pi/4))#

#=3sin(pi/2)#

Hope this was the answer you were looking for!

Answer 2 · 2018-02-21T19:11:36

See below.

Identity.

#color(red)bb(2sinAcosB=sin(A+B)+sin(A-B))#

#3(2sin(pi/4)cos(pi/4))=3(sin(pi/4+pi/4)+sin(pi/4-pi/4))#

#3(2sin(pi/4)cos(pi/4))=3sin(pi/4+pi/4)+3sin(pi/4-pi/4)#

#3(2sin(pi/4)cos(pi/4))=3sin(pi/2)+3sin(0)#

This just simplifies to:

#3sin(pi/2)#