Math Analysis CH. 3

Question

Steps on how to find the sum of 2cosx5xcos2x.

 

And 2sin3xcosx

Answer 1

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

Apply the formula cos(A + B) + cos(A - B) = 2 cosA cosB

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

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

2cos(5x) cos(2x) = cos(7x) cos(3x)

 

Answer 2

2) The trig expression is 2 sin3x cosx

Apply the formula sin(A + B) + sin(A - B) = 2 sinA cosB

In this case A = 3x and B = x

2 sin3x cosx = sin(3x + x) + sin(3x - x)

2 sin3x cosx = sin(4x) + sin(2x).