Question

students were asked to simplify the expression . two students' work is given. student a step 1: step 2: step 3: 1 tan2 θ step 4: sec2 θ student b step 1: step 2: step 3: step 4: csc2 θ part a: which student simplified the expression incorrectly? explain the errors that were made or the formulas that were misused. (5 points) part b: complete the student's solution correctly, beginning with the location of the error. (5 points) source stylesnormalfontsize

Answer 1

Student B is wrong , student A is correct in simplifying the expression .

Expression B must be simplified to cot θ .

Formulas to be used are :

1 - $sin^{2}$ θ = $cos^{2}$θ

 1 - $cot^{2}$θ = $tan^{2}$θ .

Since , location of error is step 3 , we will start from there

[ ( 1 - $sin^{2}$θ ) / sin θ ] / cos θ    = [ ( 1 - $sin^{2}$θ ) / sin θ ] * [ 1 / cos θ ]

                          = ( 1 - $sin^{2}$θ ) / ( sin θ * cos θ )

               = $cos^{2}$ θ / ( sin θ * cos θ )

                   = cot θ .

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Since , the question is incomplete we assume it to be :