Factor sec^2x-secx+tan^2x

Question

Mathematics

Marcel Hood

21 June, 20:10

Factor sec^2x-secx+tan^2x

+2

Answers (1)

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Aliya Reese · Answer 1

sec² (x) - sec (x) + tan² (x) = (sec (x) - 1) (2sec (x) + 1)

Step-by-step explanation:

sec² (x) - sec (x) + tan² (x) =

= sec² (x) - sec (x) + [sec² (x) - 1]

= sec² (x) - sec (x) + [ (sec (x) + 1) (sec (x) - 1) ]

= sec (x) [sec (x) - 1] + [ (sec (x) + 1) (sec (x) - 1) ]

= (sec (x) - 1) (sec (x) + sec (x) + 1)

= (sec (x) - 1) (2sec (x) + 1)