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5 January, 23:20

Prove this (sinx-tanx) (cosx-cotx) = (sinx-1) (cosx-1)

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  1. 5 January, 23:40
    0
    Distribute first

    sinx cosx - sinx cotx - cosx tanx+tanx cotx

    sinx cosx - sinx (cosx/sinx) - cosx (sinx/cosx) + tanx (cosx/sinx)

    sinxcosx - cosx - sinx + 1

    and factor

    cosx (sinx - 1) - 1 (sinx - 1)

    (sinx - 1) (cosx-1)
  2. 5 January, 23:43
    0
    (sinx - tanx) (cosx - cotx)

    = (sinx - sinx cosx) (cosx - cosx sinx)

    = sinx (1 - 1 cosx) cosx (1 - 1 sinx)

    = sinx (cosx cosx - 1 cosx) cosx (sinx sinx - 1 sinx)

    = sinx cosx (cosx - 1) cosx sinx (sinx - 1)

    = (cosx - 1) (sinx - 1)
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