Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Certainly! Let's go through the problem step-by-step.
We are given the equation:
[tex]\[ \sec \theta + \cos \theta = \frac{5}{2} \][/tex]
Our goal is to find the value of \( \sec \theta - \cos \theta \).
First, let's isolate \( \sec \theta \) from the given equation:
[tex]\[ \sec \theta = \frac{5}{2} - \cos \theta \][/tex]
Now we will use this expression for \( \sec \theta \) to find \( \sec \theta - \cos \theta \):
[tex]\[ \sec \theta - \cos \theta = \left( \frac{5}{2} - \cos \theta \right) - \cos \theta \][/tex]
Simplify the expression on the right-hand side:
[tex]\[ \sec \theta - \cos \theta = \frac{5}{2} - \cos \theta - \cos \theta \][/tex]
[tex]\[ \sec \theta - \cos \theta = \frac{5}{2} - 2 \cos \theta \][/tex]
Therefore, the value of \( \sec \theta - \cos \theta \) is:
[tex]\[ \sec \theta - \cos \theta = \frac{5}{2} - 2 \cos \theta \][/tex]
Hence, using the relation derived from the given condition, the expression simplifies to:
[tex]\[ \boxed{\frac{5}{2} - 2 \cos \theta} \][/tex]
We are given the equation:
[tex]\[ \sec \theta + \cos \theta = \frac{5}{2} \][/tex]
Our goal is to find the value of \( \sec \theta - \cos \theta \).
First, let's isolate \( \sec \theta \) from the given equation:
[tex]\[ \sec \theta = \frac{5}{2} - \cos \theta \][/tex]
Now we will use this expression for \( \sec \theta \) to find \( \sec \theta - \cos \theta \):
[tex]\[ \sec \theta - \cos \theta = \left( \frac{5}{2} - \cos \theta \right) - \cos \theta \][/tex]
Simplify the expression on the right-hand side:
[tex]\[ \sec \theta - \cos \theta = \frac{5}{2} - \cos \theta - \cos \theta \][/tex]
[tex]\[ \sec \theta - \cos \theta = \frac{5}{2} - 2 \cos \theta \][/tex]
Therefore, the value of \( \sec \theta - \cos \theta \) is:
[tex]\[ \sec \theta - \cos \theta = \frac{5}{2} - 2 \cos \theta \][/tex]
Hence, using the relation derived from the given condition, the expression simplifies to:
[tex]\[ \boxed{\frac{5}{2} - 2 \cos \theta} \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.