Question

Use the fundamental identities to fully simplify the expression. sin(x) cos(x) sec(x).

Answer 1

To fully simplify the expression sin(x) cos(x) sec(x), we substitute sec(x) with 1/cos(x), which then cancels with cos(x), leaving us with sin(x) as the simplified result.

Step-by-step explanation:

The question asks to simplify the expression sin(x) cos(x) sec(x) using fundamental trigonometric identities. To simplify this expression, we use the identity that sec(x) is the reciprocal of cos(x), meaning sec(x) = 1/cos(x). Now we can fully simplify the expression:

• sin(x) * cos(x) * sec(x)
• = sin(x) * cos(x) * (1/cos(x))
• = sin(x) * (cos(x)/cos(x))
• = sin(x) * 1
• = sin(x)

So the expression simplifies to sin(x).