Q : Which is 2*sin(4x)*cos(2x) written as a sum containing only sines?
A. sin 6x – sin 2x
B. sin 5x – sin3x
C. sin 5x + sin 3x
D. sin 6x + sin 2x
A: This is another product-to-sum identity, only it is an the identity that involves sines and cosines mixed. The correct identity is:
sin(a)cos(b) = [sin(a + b) + sin(a – b)]/2
Multiply the 2 across to get:
2*sin(a)cos(b) = sin(a + b) + sin(a – b)
See how this now looks like our problem?
2*sin(4x)*cos(2x)!!
So, our a = 4x and our b = 2x… Plug those in to get:
2*sin(4x)*cos(2x) = sin(4x + 2x) + sin(4x – 2x)
2*sin(4x)*cos(2x) = sin(6x) + sin(2x)
This is answer D