Question: "How to simplify sec3x−sec2x−sec⁡x+1?"

Zachariah Mcmillan

Answered question

2023-01-19

How to simplify

\sec^{3} x - \sec^{2} x - \sec x + 1

quenjvt

Beginner2023-01-20Added 4 answers

Let sec x = t, we get:

f (t) = t^{3} - t^{2} - t + 1

Since (a + b + c + d) = 0, one factor is (t - 1)
Since a - b + c - d = 0, one factor is (t - 1)
Finally

f (t) = {(t - 1)}^{2} (t + 1)

f (x) = {(\sec x - 1)}^{2} (\sec x + 1)

gibbokf5

Beginner2023-01-21Added 2 answers

\tan^{2} A = \sec^{2} A - 1

\sec^{3} x - \sec^{2} x - \sec x + 1 = \sec x (\sec^{2} x - 1) - (\sec^{2} x - 1) = (\sec x - 1) (\sec^{2} x - 1) = (\sec x - 1) \tan^{2} x

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