Sure, let's simplify the given expression [tex]\( \sec \beta \cdot \cos \beta \)[/tex].
1. Understanding the trigonometric identities:
- The secant function [tex]\( \sec \beta \)[/tex] is defined as the reciprocal of the cosine function. Thus, [tex]\(\sec \beta = \frac{1}{\cos \beta}\)[/tex].
2. Substituting the identity:
- Replace [tex]\( \sec \beta \)[/tex] with [tex]\(\frac{1}{\cos \beta}\)[/tex] in the expression. The expression [tex]\( \sec \beta \cdot \cos \beta \)[/tex] becomes:
[tex]\[
\sec \beta \cdot \cos \beta = \frac{1}{\cos \beta} \cdot \cos \beta
\][/tex]
3. Simplifying the expression:
- When [tex]\(\frac{1}{\cos \beta}\)[/tex] is multiplied by [tex]\(\cos \beta\)[/tex], the cosine functions cancel each other out. Therefore, you get:
[tex]\[
\frac{1}{\cos \beta} \cdot \cos \beta = 1
\][/tex]
Hence, the simplified expression is:
[tex]\[
\sec \beta \cdot \cos \beta = 1
\][/tex]
So, the value of the given trigonometric expression [tex]\( \sec \beta \cdot \cos \beta \)[/tex] is indeed [tex]\( 1 \)[/tex].
