Complex Numbers 17 – Proof of Sin(3A) and Cos(3A)

You’ll learn

• Prove cos 3θ = 4cos³θ − 3cos θ and sin 3θ = 3sin θ − 4sin³θ using De Moivre
• Expand (cos θ + i sin θ)³ and group the real and imaginary parts
• Equate real or imaginary parts on both sides to isolate each identity
• Use sin²θ + cos²θ = 1 to finish each proof in a single trig function