How do you simplify sec^3x-sec^2x-secx+1?

2 Answers
Nghi N.
Oct 21, 2015

Simplify: sec^3 x - sec^2 x - sec x + 1

Explanation:

Call 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)

cspark1981
Nov 2, 2015

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

Explanation:

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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