Question

Simplify the expression cos(x)sin(x)tan(x).?

A) sin(x)
B) cos(x)
C) tan(x)
D) sec(x)

Answer 1

Simplifying cos(x)sin(x)tan(x) involves using the identity tan(x) = sin(x) / cos(x) to cancel out the cos(x) terms, leaving us with sin^2(x), which does not match the given options.

Step-by-step explanation:

To simplify the expression cos(x)sin(x)tan(x), we need to recall the definition of tan(x), which is tan(x) = sin(x) / cos(x). By using this identity, we can rewrite tan(x) in terms of sin(x) and cos(x), allowing us to see which terms might cancel out. Thus, replacing tan(x) in our expression gives us:

• cos(x)sin(x)*(sin(x) / cos(x))

When we simplify this expression, the cos(x) terms will cancel each other out, leaving us with:

• sin(x)*sin(x) / 1

This simplifies further to:

• sin^2(x)

However, this result is not among the given options, indicating there might be an oversight in the available choices or possibly in the formulation of the question itself. The student should review the question context to ensure its accuracy or consult with the instructor for clarification.