Power-reducing identities.

Question

Use the power-reducing identities to rewrite the expression to one that contains a single trigonometric function of power 1. (simplify your answer.)

4sin 4x cos 4x (2cos^2 4x-1)

Answer 1

To simplify the arithmetic, let's invent a temporary variable: Let u = 4x

Then:

4 sin(u) cos (u) (2cos^2(u) -1)

= 2sin(2u) * (cos^2u + cos^2u -1)

= 2sin(2u) * ( cos^2u - sin^2u)

= 2sin(2u) * cos(2u)

= sin(4u)

= sin(16x)