Question

Use basic identities to simplify cos³(x) sin²(x) cos(x).

a) cos⁴(x)
b) cos²(x)
c) sin⁴(x)
d) sin²(x)

Answer 1

After simplifying cos³(x) sin²(x) cos(x), the result is cos³(x) - cosµ(x). The given options do not match this result, indicating a potential error in the question or options.

Step-by-step explanation:

To simplify cos³(x) sin²(x) cos(x), we have to use trigonometric identities to combine and reduce the expression. Here, we notice that cos³(x) means cos(x) * cos²(x) and we already have another cos(x) in the expression. Additionally, we note that sin²(x) is part of the Pythagorean identity, which is sin²(x) + cos²(x) = 1, thus sin²(x) = 1 - cos²(x).

Let's simplify:

• cos³(x) sin²(x) cos(x) = cos(x) * cos²(x) * sin²(x) * cos(x)
• = cos(x) * cos(x) * (1 - cos²(x)) * cos(x)
• = cos³(x) - cosµ(x)

None of the given options match cos³(x) - cosµ(x), so there may be an error in the question, or in the provided options.