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

2 Answers
Aug 6, 2018

2sin5xcos3x=sin(8x)+sin(2x)

Explanation:

We know the Product Identity

2sinAcosB=sin(A+B)+sin(AB)

Substitute , A=5xandB=3x

2sin5xcos3x=sin(5x+3x)+sin(5x3x)

2sin5xcos3x=sin(8x)+sin(2x)sum of trig. functions.

Aug 6, 2018

sin8x+sin2x

Explanation:

using the product to sum formula

x2sinxcosy=sin(x+y)+sin(xy)

here x=5x and y=3x

2sin5xcos3x

=sin(5x+3x)+sin(5x3x)=sin8x+sin2x