Final answer:
To evaluate the integral of cos²θ, the double angle formula is used, leading to an integral of ½θ + ¼sin(2θ) + C, which is not provided in the given options. Hence, the correct answer is not listed among the options.
Step-by-step explanation:
To evaluate the integral ∫cos²θ dθ using the double angle formula, we can use the identity given by:
cos(2θ) = cos²θ - sin²θ
Rewriting the right-hand side, we get:
cos(2θ) = 2cos²θ - 1 or cos²θ = ½ + ½ cos(2θ)
Thus, the integral becomes:
∫cos²θ dθ = ∫(½ + ½ cos(2θ)) dθ = ½θ + ¼sin(2θ) + C
So none of the provided options are correct. The correct evaluation of the integral is θ/2 + sin(2θ)/4 + C, where C is the constant of integration.