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31 October, 04:15

How to prove (1-secx) / (1-cosx) = - secx

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Answers (2)
  1. 31 October, 05:14
    0
    To answer, we have to simplify the expression given. We know that:

    sec x=1/cos x

    1-sec x = 1-1/cos x = (cos x - 1) / cos x

    (1-sec x) / (1-cos x) = (cos x - 1) / (cos x * (1-cos x)) = - 1/cos x = - sec x
  2. 31 October, 06:13
    0
    Hello,

    We suppose x ≠+/-π/2. (division by 0)

    sec x=1/cos x

    1-sec x = 1-1*cos x = (cos x - 1) / cos x

    (1-sec x) / (1-cos x) = (cos x - 1) / (cos x * (1-cos x)) = - 1/cos x = - sec x
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