Question

For all real numbers x, what is the value of cos²(x) - sin²(x)?

- a) cos(2x)
- b) cos²(2x)
- c) 1
- d) sin(2x)

Answer 1

The value of cos²(x) - sin²(x) is equal to cos(2x) (Option a).

Step-by-step explanation:

Trigonometric Identity: Use the identity cos(2θ) = cos²(θ) - sin²(θ).

Comparison: Notice the similarity between the given expression and the identity.

Identify θ: In this case, θ = x, so cos(2θ) = cos(2x).

Final Answer: The value of cos²(x) - sin²(x) is cos(2x), confirming Option a.