Evaluate 1 – cos(θ) – cos(θ)

To evaluate the expression 1 – cos(θ) – cos(θ), we can simplify it first.

Let’s combine the terms involving cos(θ):

1 – cos(θ) – cos(θ) = 1 – 2cos(θ)

This means the expression simplifies to 1 – 2cos(θ).

Now, the value of 1 – 2cos(θ) will depend on the specific angle θ we are evaluating. The cosine function varies between -1 and 1 for real values of θ. Therefore:

• If cos(θ) = 1, then 1 – 2cos(θ) = 1 – 2(1) = -1.
• If cos(θ) = -1, then 1 – 2cos(θ) = 1 – 2(-1) = 3.
• If cos(θ) = 0, then 1 – 2cos(θ) = 1 – 2(0) = 1.

So, depending on the value of cos(θ), the resulting value of the expression 1 – cos(θ) – cos(θ) will vary accordingly. In general, the expression represents a linear transformation of the cosine function that can take values between -1 and 3 based on the input angle θ.