Use the power reducing_formulas to rewrite sin 3x cos3x in terms of the first power of cosine.

Question

Simplify your answer as much as possible.
Step by step solutions

Answer 1

1. Use the power reducing formula: sin^2 A + cos^2 A = 1

2. Substitute sin^2 3x for (1 - cos^2 3x): sin 3x cos 3x = (1 - cos^2 3x)cos 3x

3. Use the power reducing formula: cos 2A = cos^2 A - sin^2 A

4. Substitute cos^2 3x - sin^2 3x for cos 2x: sin 3x cos 3x = (1 - cos^2 3x)(cos^2 3x - sin^2 3x)

5. Simplify: sin 3x cos 3x = cos^3 3x - sin^3 3x