Question

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

Answer 1

To fully simplify sin(-x)cos(-x)sec(-x), you can use the trigonometric identity sec(x) = 1/cos(x) along with the fact that sine and cosine functions are odd functions.

Step-by-step explanation:

To fully simplify sin(-x)cos(-x)sec(-x) using the fundamental identities, we can start by using the trigonometric identity:
sec(x) = 1/cos(x)

Next, since sine and cosine functions are both odd functions, we have:
sin(-x) = -sin(x) and cos(-x) = cos(x)

Therefore, sin(-x)cos(-x)sec(-x) = (-sin(x))(cos(x))(1/cos(x)) = -sin(x)