Students were asked to prove the identity (tan x)(sin x) = sec x - cos x

Students were asked to prove the identity (tan x)(sin x) = sec x - cos x. Two students' work is given. Student A Student B Step 1: Sinx 1 -. sin x = sec x - Cos x Step 1: tan x sinx = - COS X COS X COS X Step 2: sin x 1 COs x = sec x - cos x Step 2: tan x sinx = COS X COS X COS X Step 3: 1-cos x = sec x - Cos x Step 3: tan xsinx = 1-cosx COS X COS X Step 4: 1 cos x = sec x - cos x |Step 4: tan xsin x = sin2x COS X COS X COS X Step 5: sec x - cos x = sec x - Cos x Step 5: tan x sinx = - sin x . sin x COS X Step 6: tan x sin x = tan x sin 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)