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 A
Step 1: secant theta over secant theta minus cosine theta over secant theta
Step 2: 1 minus cosine theta over the quantity 1 over cosine theta end quantity
Step 3: 1 − cos2 θ
Step 4: sin2 θ Student B
Step 1: the quantity 1 over cosine theta end quantity minus cosine theta over the quantity secant theta
Step 2: the quantity 1 minus cosine squared theta end quantity over cosine theta all over secant theta
Step 3: sine squared theta over cosine squared theta
Step 4: tan2 θ
Part 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)
