Question

PLEASE HELP !! 51 POINTS !!

Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given.

Student A

Step 1: cosecant theta over cosecant theta minus sine theta over cosecant theta

Step 2: 1 minus sine theta over the quantity 1 over sine theta end quantity

Step 3: 1 − sin2 θ

Step 4: cos2 θ

Student B

Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta

Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta

Step 3: cosine squared theta over sine squared theta

Step 4: cot2 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)

Answer 1

Student B

Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta

Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta

Step 3: cosine squared theta over sine squared theta

Step 4: cot2 θ

Explanation: