Math Analysis Ch.3

Question

steps on how to express 2cos5xsin2x as a sum.

Answer 1

The trig expression is 2cos(5x) sin(2x)

sin(A + B) - sin(A - B) = 2 cosA sinB

In this case A = 5x and B = 2x

2cos(5x) sin(2x) = sin(5x + 2x) - sin(5x - 2x)

= sin(7x) - sin(3x)

2cos(5x) sin(2x) = sin(7x) - sin(3x).