Question

URGRENNTTT PLSS HELPP 50 POINTSS!!!!! Students were asked to simplify the expression cotangent theta plus tangent theta over cotangent theta. Two students' work is given.
Student A

Step 1: cotangent theta over cotangent theta plus tangent theta over cotangent theta

Step 2: 1 plus tangent theta over the quantity 1 over tangent theta end quantity

Step 3: 1 + tan2 θ

Step 4: sec2 θ Student B

Step 1: the quantity 1 over tangent theta end quantity plus tangent theta over the quantity cotangent theta

Step 2: the quantity 1 plus tangent squared theta end quantity over tangent theta all over cotangent theta

Step 3: secant squared theta over tangent squared theta

Step 4: csc2 θ

Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)

Answer 1

The student that simplified the expression incorrectly is student 2

How to determine the incorrect result?

The steps are given as:

$\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}$

Student 1:

• Step 1: $\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}$
• Step 2: $1 + \frac{\tan(\theta)}{\cot(\theta)}$
• Step 3: 1 + tan²(Ф)
• Step 4: sec²(Ф)

Student 2:

• Step 1: $\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}$
• Step 2: $\frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}$
• Step 3: sec²(Ф)/tan²(Ф)
• Step 4: csc²(Ф)

As a general trigonometry rule;

$\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)$

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:

$\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}$

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:

brainly.com/question/8120556

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