Question

Cos²a-cos2a A) sin²a. B) -sin²a. C) 0. D) -1

Answer 1

Ответ:

А) sin²a

решение на фото

Answer 2

To simplify the expression cos²a - cos2a, you can use trigonometric identities.

First, recognize that cos2a can be expressed in terms of cos²a using the double-angle identity:

cos2a = 2cos²a - 1

Now, substitute this into the original expression:

cos²a - (2cos²a - 1)

Now, distribute the negative sign:

cos²a - 2cos²a + 1

Combine like terms:

• cos²a + 1

Now, notice that 1 - cos²a is equal to sin²a, as it's one of the fundamental trigonometric identities (sin²a + cos²a = 1). So, we have:

• cos²a + 1 = -sin²a + 1

Now, subtract 1 from -sin²a + 1:

-1 - sin²a

So, the simplified expression is -1 - sin²a, which corresponds to option (D) -1.