Which of the following is incorrect? A cos 20 = cos² 0- sin² 0 B C cos 2012 sin² 0 C cos 20-1- cos² 0 D None of these

To determine which of the given options is incorrect, we will analyze each option step by step.

Option A: cos 20 = cos² 0 - sin² 0 This is a trigonometric identity known as the cosine double-angle formula. It states that cos 2θ = cos² θ - sin² θ. However, in this option, we have cos 20 on the left side, which is not equal to cos² 0 - sin² 0. Therefore, option A is incorrect.

Option B: This option is not provided, so we cannot determine if it is correct or incorrect.

Option C: cos 2012 sin² 0 This expression involves the sine function, but it does not have any cosine terms. Since the question asks for an incorrect option, and this option does not include a cosine term, it is incorrect.

Option D: cos 20 - 1 - cos² 0 This expression involves both the cosine and sine functions. However, we can simplify it using trigonometric identities. cos 20 - 1 can be rewritten as cos 20 - cos² 0 + sin² 0 using the Pythagorean identity sin² θ + cos² θ = 1. Now, we have cos 20 - cos² 0 + sin² 0 - cos² 0. By rearranging the terms, we get cos 20 - 2cos² 0 + sin² 0. Since this expression involves both cosine and sine terms, it is not equal to any of the given options. Therefore, option D is also incorrect.

In conclusion, options A, C, and D are incorrect.