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21 June, 20:10

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

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  1. 21 June, 21:53
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    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)
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