100 POINTS + BRAINLIEST PLEASE HELP!!!!
Students were asked to prove the identity (cot x)(cos x) = csc x − sin x. Two students' work is given.
Student A
Step 1: cosine x over sine x times cosine x equals cosecant x minus sine x
Step 2: cosine squared x over sine x equals cosecant x minus sine x
Step 3: 1 minus sine squared x over sine x equals cosecant x minus sine x
Step 4: 1 over sine x minus sine squared x over sine x equals cosecant x minus sine x
Step 5: csc x − sin x = csc x − sin x Student B
Step 1: cotangent x times cosine x equals 1 over sine x minus sine x
Step 2: cotangent x times cosine x equals 1 over sine x minus sine squared x over sine x
Step 3: cotangent x times cosine x equals 1 minus sine squared x over sine x
Step 4: cotangent x times cosine x equals cosine squared x over sine x
Step 5: cotangent x times cosine x equals cosine x over sine x times cosine x
Step 6: cot x cos x = cot x cos x
Part A: Did either student verify the identity properly? Explain why or why not. (10 points)
Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 points)
