The conversation between human and AI assistant.
What is the formula for quadruple angle?
Can you explain how to derive that formula?
Sure, the formula can be derived using the double angle formula: sin(2θ) = 2sin(θ)cos(θ). If you substitute 2θ for θ, you get: sin(4θ) = 2sin(2θ)cos(2θ). Since cos(2θ) = 1 - 2sin²(θ), you can replace it in the equation and get sin(4θ) = 2sin(2θ)(1 - 2sin²(θ)). Solving for sin(4θ), you get the formula: 4θ = 2sin(2θ).