Find the algebraic expression that is equal to sec theta - cos (-theta)

To find the algebraic expression that is equal to sec(theta) - cos(-theta), we need to recall the definitions of secant and cosine functions.

Secant function is the reciprocal of the cosine function, so sec(theta) = 1/cos(theta).

The negative of an angle (-theta) is equivalent to rotating that angle by 180 degrees, which does not affect the value of the cosine function. Therefore, cos(-theta) = cos(theta).

Substituting these values, we have sec(theta) - cos(-theta) = 1/cos(theta) - cos(theta).

So, the algebraic expression that is equal to sec(theta) - cos(-theta) is 1/cos(theta) - cos(theta).

To find the algebraic expression equal to sec(theta) - cos(-theta), we need to understand the trigonometric definitions and identities involved.

1. First, let's start with sec(theta). The secant function is defined as the reciprocal of the cosine function: sec(theta) = 1 / cos(theta).

2. Next, we need to consider cos(-theta). According to the evenness property of cosine, cos(-theta) is equal to cos(theta).

Now, substituting cos(-theta) in place of cos(theta) in our expression, we have sec(theta) - cos(-theta) = sec(theta) - cos(theta).

Therefore, the algebraic expression equal to sec(theta) - cos(-theta) is sec(theta) - cos(theta).

using what I showed you earlier, what do you get?