precalc

tanx cotx
------- + ------- = 1 +secxcscx
1 - cotx 1- tanx

prove the proof

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  1. tanx/(1-cotx) + cotx/(1-tanx)
    = tanx/(1-cotx) + cotx/(1-tanx) * (-tanx/-tanx)
    = tanx/(1-cotx) - tan^2x/(1-tanx)
    = (cotx-tan^2x)/(1-tanx)
    = (1-tan^3x)/(tanx(1-tanx))
    = (1-tanx)(1+tanx+tan^2x) / (1-tanx)(tanx)
    = (1+tanx+tan^2x)/tanx
    = 1/tanx + 1 + tanx
    = 1 + sinx/cosx + cosx/sinx
    = 1 + (sin^2x+cos^2x)/(sinx cosx)
    = 1 + secx cscx

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  2. oops . typo in line 2, but you should be able to catch it.

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