IDNLearn.com offers a seamless experience for finding and sharing knowledge. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
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].
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].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.