Question

Students were asked to simplify the expression the quantity secant theta minus cosine theta end quantity over secant period Two students' work is given.Student AStep 1: secant theta over secant theta minus cosine theta over secant thetaStep 2: 1 minus cosine theta over the quantity 1 over cosine theta end quantityStep 3: 1 − cos2 θStep 4: sin2 θStudent BStep 1: the quantity 1 over cosine theta end quantity minus cosine theta over the quantity secant thetaStep 2: the quantity 1 minus cosine squared theta end quantity over cosine theta all over secant thetaStep 3: sine squared theta over cosine squared thetaStep 4: tan2 θPart A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)

Answer 1

Error part:

There is a mistake with student B in step 3 so I start with step 2

`\begin{gathered} Step\text{ 2 }((1-cos^2\emptyset)/(cos\emptyset))/(sec\emptyset) \\ \\ Step\text{ 3 }(1-cos^2\emptyset)/(cos\emptyset *sec\emptyset) \\ \\ Step\text{ 4 1-cos}^2\emptyset \\ Step\text{ 5 sin}^2\emptyset \end{gathered}`