Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.Student AStep 1:1/Cos x * 1/sin x = cot x + tan xStep 2: 1/cos x sin x = cot x + tan xStep 3: (cos^2 x + sin^2 x)/cos x sin x = cot x + tan xStep 4: cos^2 x/cos x sin x + sin^2x/cos x sin x= cot x + tan xStep 5: cos x/sin x + sin x/cos x = cot x + tan xStep 6: cot x + tan x = cot x + tan xStudent BStep 1: sec x csc x = cos x/ sin xStep 2: sec x csc x = cos^2x/cos x sin x + sin^2x/cos x sin xStep 3: sec x csc x = cos^2x + sin^2x/cos x sin xStep 4: sec x csc x = 1/cos x sin xStep 5: sec x csc x = (1/cos x), (1/sin x)Step 6: sec x csc x = sec x csc xPart 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.
Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.
Student A
Step 1:1/Cos x * 1/sin x = cot x + tan x
Step 2: 1/cos x sin x = cot x + tan x
Step 3: (cos^2 x + sin^2 x)/cos x sin x = cot x + tan x
Step 4: cos^2 x/cos x sin x + sin^2x/cos x sin x= cot x + tan x
Step 5: cos x/sin x + sin x/cos x = cot x + tan x
Step 6: cot x + tan x = cot x + tan x
Student B
Step 1: sec x csc x = cos x/ sin x
Step 2: sec x csc x = cos^2x/cos x sin x + sin^2x/cos x sin x
Step 3: sec x csc x = cos^2x + sin^2x/cos x sin x
Step 4: sec x csc x = 1/cos x sin x
Step 5: sec x csc x = (1/cos x), (1/sin x)
Step 6: sec x csc x = sec x csc x
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.
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