Question

When does cos(θ) equal cos(2θ)?

a) Always
b) Never
c) Only when θ is an odd multiple of π/2
d) Only when θ is an even multiple of π/2

Answer 1

Cos(θ) equals cos(2θ) at certain angles, but this situation cannot be generalized to always, never, or at specific multiples of π/2 without further algebraic solutions taking into account the periodic nature of the cosine function.

Step-by-step explanation:

The question 'When does cos(θ) equal cos(2θ)?' is related to understanding the properties of trigonometric functions like the cosine function. In general, cos(θ) does not always equal cos(2θ), as they are two different functions with different periods. However, there are specific angles for which they might be equal.

To find out when cos(θ) equals cos(2θ), we can set up an equation cos(θ) = cos(2θ) and solve for θ. Without getting into the detailed algebra, we would typically use trigonometric identities like the double-angle formula for cosine, which is cos(2θ) = cos2(θ) - sin2(θ), or one of its equivalent forms. Nevertheless, the general solution for this kind of trigonometric equation would involve multiple steps that consider the periodic nature of the cosine function.

Thus, the answer requires more than a simple selection from given options and would not be found among the provided options which suggest specific multiples of π/2. It would depend on the context and the method used to solve the trigonometric equation.