How could I turn 2sin5xcos3x into a sum of trig functions?

2 Answers
Aug 6, 2018

#2sin5xcos3x=color(red)(sin(8x)+sin(2x)#

Explanation:

We know #"the "color(blue)"Product Identity"#

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

Substitute , #A=5x and B=3x#

#2sin5xcos3x=sin(5x+3x)+sin(5x-3x)#

#2sin5xcos3x=color(red)(sin(8x)+sin(2x)larr"sum of trig. functions."#

Aug 6, 2018

#sin8x+sin2x#

Explanation:

#"using the "color(blue)"product to sum formula"#

#•color(white)(x)2sinxcosy=sin(x+y)+sin(x-y)#

#"here "x=5x" and "y=3x#

#2sin5xcos3x#

#=sin(5x+3x)+sin(5x-3x)=sin8x+sin2x#