Question Find $\sec(-x)$ if $\sec(x)=2$ .

Studdy Solution

STEP 1

Assumptions
1. $\sec(x) = \frac{1}{\cos(x)}$
2. $\sec(-x) = \frac{1}{\cos(-x)}$
3. $\cos(-x) = \cos(x)$ (cosine is an even function)
4. Given that $\sec(x) = 2$ , we need to find $\sec(-x)$

STEP 2

Since $\sec(x) = 2$ , we can write it as:
$\sec(x) = \frac{1}{\cos(x)} = 2$

STEP 3

To find $\sec(-x)$ , we use the property of the cosine function being even, which means $\cos(x) = \cos(-x)$ .

STEP 4

Using the definition of secant in terms of cosine for $\sec(-x)$ :
$\sec(-x) = \frac{1}{\cos(-x)}$

STEP 5

Substitute $\cos(-x)$ with $\cos(x)$ due to the even property of cosine:
$\sec(-x) = \frac{1}{\cos(x)}$

STEP 6

Since we know $\sec(x) = 2$ , and $\sec(x) = \frac{1}{\cos(x)}$ , we can substitute $\frac{1}{\cos(x)}$ with 2:
$\sec(-x) = 2$
Thus, $\sec(-x) = 2$ .

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