Verify that 1 + cos 2 theta / 2 cos theta = cos theta is an identity

(1 + cos (2theta)) / 2cos (theta)

cos (2theta) = 2cos² (theta) - 1

(1 + 2cos² (theta) - 1) / 2cos (thetal

2cos² (theta) / 2cos (theta)

cos (theta)

Answer and Step-by-step explanation:

We want to verify that (1 + cos (2θ)) / 2cos (θ) = cos (θ).

Let's focus on the left side. Look at cos (2θ). This is an identity, so remember that cos (2θ) = cos²θ - sin²θ. Also, look at the 1. Remember that sin²θ + cos²θ = 1, so plug both of these expressions into our equation:

(1 + cos (2θ)) / 2cos (θ) = ? cos (θ)

((sin²θ + cos²θ) + (cos²θ - sin²θ)) / 2cos (θ) = ? cos (θ)

2cos²θ / 2cosθ = ? cosθ

cosθ = cosθ

Thus, we have proved this is an identity.