Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.

Student A Student B Step 1: = cot x + tan x Step 1: sec xcsc x = COS X sin x cosx sinx sin x COS X Step 2: = cotx + tan x Step 2: sec xcsc X = cos- x sin~ x cos x sin x cos xsinx cosxsinx Step 3: cos x + sin x = cot x + tan x Step 3: sec xcsc X = cos x + sin x cos x sin x cos x sin x Step 4: cos* x sin x = cotx + tan x Step 4: secxcsc * = cos x sin x cos x sin x cos x sin x Step 5: COS X sin x = cotx + tan x Step 5: sec xcsc x = sin x COS X COS X sin x Step 6: cot x + tan x = cot x + tan x Step 6: sec x csc x = sec x CSC X