Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
The student that simplified the expression incorrectly is student 2
How to determine the incorrect result?
The steps are given as:
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}[/tex]
Student 1:
- Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]
- Step 2: [tex]1 + \frac{\tan(\theta)}{\cot(\theta)}[/tex]
- Step 3: 1 + tan²(Ф)
- Step 4: sec²(Ф)
Student 2:
- Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]
- Step 2: [tex]\frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]
- Step 3: sec²(Ф)/tan²(Ф)
- Step 4: csc²(Ф)
As a general trigonometry rule;
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)[/tex]
This means that student 1 is correct, while student 2 is not
The first error in student 2's workings is in step 2, where we have:
[tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]
The above expression is not justified and cannot be proved by any trigonometry rule
Since the step 2 is incorrect, the other steps cannot be used.
Hence, the student that simplified the expression incorrectly is student 2
Read more about trigonometric expressions at:
https://brainly.com/question/8120556
#SPJ1
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.