Use the power reducing_formulas to rewrite sin 3x cos3x in terms of the first power of cosine.
Simplify your answer as much as possible.
Step by step solutions
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