There is more than one way to show the Double-Angle Identity for cosine. Which method is NOT a representation of cos(60∘) using the Double-Angle Identity?

Question

Answer 1

Hi Raquel R.,

The three Double-Angle Formulas for cos(2θ) are:

cos(2θ) = cos²(θ) - sin²(θ)

cos(2θ) = 1 - 2sin²(θ)

cos(2θ) = 2cos²(θ) - 1

Therefore:

cos(60⁰) = cos(2*30⁰) = 2sin²(30⁰) - 1; (this is not one of the formulas for cos(2θ), false).

cos(60⁰) = cos(2*30⁰) = 2cos²(30⁰) - 1; (true)

cos(60⁰) = cos(2*30⁰) = cos²(30⁰) - sin²(30⁰); (true)

cos(60⁰) = cos(2*30⁰) = 1 - 2sin²(30⁰) - 1: (true).

I hope this helps, Joe.