Question

Students were asked to prove the identity (cot x)(cos x) = csc x − sin x. Two students' work is given.Part A: Did either student verify the identity properly? Explain why or why not.Part B: Name two identities that were used in Student A's verification and the steps they appear in.

Answer 1

Part A

Looking at the work done by each student, both students verified the identity properly because the trigonometric identities were properly applied where necessary, the steps were clear, mathematical operations were applied correctly and at the end, both sides of the equation were the same.

Part B

Looking at student's A verification,

In step 3, the pythagorean identity was used

In step 5, the reciprocal identity was used