Question

Write each sum or difference as a product with positive arguments -4(sin4x - sin2x) A) 8cos 3xsin x B) 8sin xsin 3x C) -8cos 3xsin x D) 8cos 3xcos x

Answer 1

C) -8cos 3xsin x

Explanation:

To express -4(sin4x - sin2x) as a product, we use the formula sinA - sinB = 2cos[(A + B)/2]sin[(A - B)/2.

Comparing sin4x - sin2x with sinA - sinB, A = 4x and B = 2x.

Substituting these into the equation, we have

sin4x - sin2x = 2cos[(4x + 2x)/2]sin[(4x - 2x)/2

sin4x - sin2 x = 2cos[6x/2]sin[2x/2]

sin4x - sin2x = 2cos3xsinx

So, -4(sin4x - sin2x) = -4(2cos3xsinx) = -8cos3xsinx

So, -4(sin4x - sin2x) = -8cos3xsinx

Thus, the answer is C