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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
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